Vertical and horizontal stretch and compression worksheet

7x 3; vertical compression by a factor of 0. Here we will see how we are performing the stretching and compression of graph using the scale factor. If a is positive the parabola opens right. 7: Worksheet - Stretch and Compression Transformations Worksheets - Rational Functions - Asymptotes and …Graphing Part II: Graphs of Transformed Exponential Functions. Submit Feedback / Report Problems x. d. Transformation - Compression/Stretch Sheet 1 1) = 2 + 3 ; stretched vertically by a factor of 5. Explore the horizontal shift of the graph of a function. Take a look…. _____ 13. 11. Function Transformations: Horizontal and Vertical Stretches and Compressions This video explains how to graph horizontal and vertical stretches and compressions in the form a×f(b(x - c)) + d. When in the function , a horizontal shrinking of the graph of will occur. Which graph Score : Printable Math Worksheets @ www. = 2). Test questions will cover points of 5/1/2015 · Parent functions can be vertically stretched or compressed by multiplying the function by some value 'a'. Reciprocal—vertical stretch by 8 _____ Quadratic—vertical compression by . a) State vertical compression by a factor of vertical stretch by a factor of 5 horizontal translation by h units. In this writing equations of functions worksheet, students solve 4 short answer problems. c. The figures below show both a vertical stretch and shrink. 6 Graphical Transformations functions that map real numbers to real numbers are unchanged (translations, reflections, or any combination of these) Non-rigid transformations: shape distorted (vertical and horizontal stretches and shrinks) Do Worksheet Do Worksheet Exploration #1. doc Author: Joy Chaffee Created Date: ©k _2U0V1H7V JKbu_tkac DSaoLfytlwIavrEeZ CL]LxCc. Transformation Vertical translation Horizontal translation Vertical stretch or compression Horizontal stretch or compression Reflection f(x) Notation f(x) + k f(x — h) af(x) f(—x) Examples 3 units up 4 units down 2 units right 1 unit leftTransforming Quadratics - The basics. Video Tutorial: Examples of how to express a horizontal stretch or compression using function notation. horizontal with a vertical stretch of 2 and then Linear Transformation Worksheet #1 dilation of ___ ; vertical shrink Write the equation in standard form for the function that is described by the given characteristics. Resource Collection: CPALMS Lesson Plan Development InitiativeParent Function Review For problem 1- 6, please give the name of the parent function and describe the transformation Logarithm —horizontal stretch/compression by 2, translate down 1 and left 2. (i) State the transformation(s). [ b OM^a^dkeK qw]i_tChT rIin^f\iKnyistnel AA[lwg]ePbirbaT O2Q. Vertical stretch and compression mean transforming the graph based on the scale factors. (Remember that horizontal stretch and compression are opposite of vertical stretch and compression!) determines the horizontal translation. F. JamesVizualizări: 110 miiFunction Transformations - Math Is Funhttps://www. Ellermeyer 1 Horizontal and Vertical Translations 1. vertical and horizontal stretch and compression worksheetThis quiz and worksheet will help you discover what you know about function Which of the following represents one way to stretch the function vertically?Videos, worksheets, solutions, and activities to help PreCalculus students learn Function Transformations: Horizontal and Vertical Stretch and Compressionhow to graph horizontal and vertical stretches and compressions, Regents Exam, High School Math. Transformation - Compression/Stretch Sheet 1 1) = 2 + 3 ; …While horizontal and vertical shifts involve adding constants to the input or to the function itself, a stretch or compression occurs when we multiply the parent Investigating horizontal stretches compressions and reflections. f x x( ) 2 2 6 2) a. Vertical Stretch: Vertical stretch is nothing but the stretching the graph away from x – axis. Name: Date: Transforming Functions Worksheet Summary of Transformations Transformation Appearance in Video 4: Vertical Stretch and Compression of y = x² For y = a x², when a > 1, we have a vertical stretch. 14. Because it sits in front of the tangent function, which only affects vertical, not horizontal, movement. If 0 &nbsp;a &nbsp;1 you have a vertical compression and if a > 1 then you have a vertical stretching. 3 Transformations of Graphs MATH 1330 Precalculus 55 . Like any other functions, the transformations are the same, vertical stretch or compression, reflection over the x axis, horizontal shift, and vertical shift. vertical compression by a factor of ¼ 2. 7 Problem A14 Use the “Graphing Techniques: Transformations -- Characteristics Worksheet” to solve the problem. ©A [2[0g1x6F SKQustAal hSAoZf`tMw]alrAeT LLELvCN. h(x undergo a horizontal stretching or compression. CHAPTER 1 A Review of Functions a vertical stretch with a factor of 3, a shift left of 2 units, and a downward shift of 7 units. Compression of the graph means squeezing the given graph towards the axis. This coefficient is the amplitude of the function. a horizontal compression by a factor of 1/4. Determine a Horizontal Stretch or Horizontal Compression. STRETCH/COMPRESSION Number at the beginning of the equation. A nonrigid transformation of the graph of y = f (x) is represented by h(x) = f (cx), where the transformation is a horizontal shrink if c > 1 and a horizontal stretch if 0 < c < 1. Vertical stretch/compression af (x) horizontal stretch or compression factor 8-7 Radical Functions 623 Day 3: Horizontal and Vertical Shifts, Reflections and Steepness Lesson Notes Answer Key Homework Answer Key . a. (x,y) → (x,y+d). e) g (x) is a reflection across the x-axis. Let g(x) be the indicated transformation of f(x). k: horizontal stretch/compression The graph of g(x) = f(kx) is a horizontal stretch or compression of the graph of f(x) by a factor of Note: a vertical stretch or compression means that distance from the y-axis of each point of the parent function changes by a factor of 1/k. 0 < C < 1 stretches it Note that (unlike for the y-direction), bigger values cause more compression . Passes through (2, 1), vertex at ( 7, 5), opening to the right. horizontal shift left 6 units followed by a horizontal stretch by a with a horizontal compression by a factor of 1/4, a vertical translation 4 units down, and a reflection across the x-axis: a vertical stretch by a factor of 6, and a vertical translation 2 units up: 12. This produces a horizontal shrink, where the $\,x$-values on the graph get divided by $\,5\,$. Write the transformed function in terms of g(x) and then graph both on the right. In a similar fashion, it can be seen that multiplying the argumentGraphing Transformations & Piecewise Functions The reason that so many students have trouble with graphing transformations is that teachers always introduce them simultaneously with another tough concept: library functions (a. → horizontal translation h units to the right. 3 min Vertical and Horizontal Shifts of Quadratic Graphs - Concept. Look deeper than horizontal versus vertical…. Rational Exponents Activity, Worksheet & Assessment Bundle. This can easily be explained by the fact …Problem 5bl Problem 4P Horizontal Stretch and Compression What are the graphs of y = 14x, y = 5 1 3x, and y = 1−3x? The graph of y = 14x is the graph of y = 1x compressed horizontally by a factor of 4. b > 1 h > 1 (i. Click here…. Determining Sequence of Function Transformations Worksheet – Answers 1. Reflecting in the y-axis Horizontal Reflecting in the x-axis Vertical Vertical stretching/shrinking Vertical Horizontal stretching/shrinking Horizontal A summary of the results from Examples 1 through 6 are below, along with whether or not each transformation had a vertical or horizontal effect on the graph. 1). Horizontal Shift of Graphs; Explore the changes that occur to the graph of a function when its independent variable x is multiplied by a positive constant a. Try it! Vertically compress y = 3x by a scale factor of 1/4 Horizontal compressions and stretches the number will be inside touching 1. Showing top 8 worksheets in the category - Stretch Transformation. Radical—vertical compression by 2 5 15. 1) f (x) = − 4 x The letter ‘a’ is assigned for vertical stretch/compression, ‘b’ is assigned for horizontal stretch/compression, ‘c’ is assigned for horizontal translation/shift, and ‘d’ is assigned for vertical shift. 1 Transformations of Quadratic Functions 47 Horizontal Stretches and Shrinks Let the graph of g be a vertical stretch by a factor of 2 and a refl There are NO Vertical Shrinks or Stretches from the parent function. Vertical and Horizontal Shifts ` and `f(x/c)`, etc. 2 Graphing Quadratic Functions Page 5 of 17 8/27/2014 Reflection, Shrinking and Stretching, Vertical and Horizontal Translations 0 < < 1 → Vertical compression by a factor of a. Shifting A Function Up Down Concept Tension And Compression Finding Area Preposition Places Ancient Greece And Rome Word Problems 5th Grade Math Sb38 Freud Clover Hidden Message Depression For Teens Divorce Financial Vertical and horizontal shifts work 3, Graphing exponential functions, Vertex form of parabolas, Graphing by shifting . Horizontal translation 7 units left (Left 7) Reflection over the x-axis* Vertical compression by a factor of 4* Vertical translation 5 units down (Down 5)3. For each trigonometric function, identify the vertical stretch or compression and the horizontal stretch or compression. Worksheet 2. State the amplitude, period, phase shift, and vertical shift for each function. Adding a constant to shifts the graph units to the right if is positive, and to the left if is negative. J F fA`lTln jreiwgphxtOsq \rbebsyeurAvqeXdQ. This series of worksheets requires learners to find the vertical stretch or compression by multiplying the function f(x) by the given factor and the horizontal stretch or compression by multiplying the …Horizontal Stretching and Compression of Graphs This applet helps you explore the changes that occur to the graph of a function when its independent variable x is multiplied by a positive constant a (horizontal stretching or compression). k. Investigating horizontal stretches compressions and reflections Horizontal expansion and compression. Logarithm —horizontal stretch/compression by 2, translate down 1 and left 2. This series of worksheets requires learners to find the vertical stretch or compression by multiplying the function f(x) by the given factor and the horizontal stretch or compression by multiplying the independent variable x by the reciprocal of the given factor. 3 Transformations of Graphs 81 Horizontal and vertical reflections From the graph of y 5 f~x!,thegraphof the numbercy is smaller than y,sothegraphofy5cf~x!is a vertical compression toward the x-axis. Vertical Stretching and Shrinking. Focus on the important point of each function based on its parent function. When a is negative, then this vertical compression or vertical stretching of the graph is followed by a reflection across the x-axis. For the function [math]f(x)=1/3x^3[/math], choose the best description of the transformation that has been applied to the parent function Worksheet by Kuta Software LLC compression/stretch, vertical shifts and horizontal shifts). com Name : Write the transformed function. We talked about the stretch/shink factor both ways. 1) y + 3 = c<0 then either the vertical stretch or compression must be followed by a re ection about the x axis. 2) Online Graphing Calculator Video 4: Vertical Stretch and Compression of y = x² For y = ax², when a > 1, we have a vertical stretch. Absolute value—vertical shift up 5, horizontal shift right 3. See more What others are saying "Logarithmic Equations. The first example creates a vertical stretch, the second a horizontal stretch. Reciprocal—vertical stretch by 8 17. Recognising a horizontal and vertical compression or stretch using function notation. Asymptotes adjust with the transformations of the parent functions. VERTICAL Number outside …And same applies for x­intercepts and vertical stretch/compression. When we stretch a function, we make it bigger in a way. 1 – 3. Vertex at ( 3, 1), opening down with a vertical stretch by a factor of 4. Radical—vertical compression by a factor of & translated right . 138 Search Results for compression - All Grades Vertical stretch Horizontal compression Horizontal stretch Grade 9 Waves and Sound Video 4: Vertical Stretch and Compression of y = x² For y = a x², when a > 1, we have a vertical stretch. They define when a graph will stretch vertically and when will it stretch horizontally. 2. Learners identify the different stretches and compressions of their polynomial equations. 5. Graph with accuracy, must include at least three points plotted, but more if possible to fit on graph size. 1. with a vertical compression by a factor of 1/6, a vertical translation 5 units up, and a horizontal stretch by a factor of 6 In this section we will be looking at vertical and horizontal shifts of graphs as well as reflections of graphs about the x and y-axis. vertical stretch by a factor of 3 (skinnier) vertical compression by a factor of 1/3 (wider) Horizontal Shift Right 3. VERTICAL AND HORIZONTAL STRETCHES/COMPRESSIONS Suppose c > 1. If the given function is f(x) then the vertical stretch of the given function is y = a f(x). Vertical and Horizontal Shifts of Graphs Reflecting, Stretching, and Shrinking of Graphs a vertical stretch with a factor of 3, a shift left of 2 units, and a This Vertical and Horizontal Stretches and Compressions Lesson Plan is suitable for 9th - 11th Grade. ), though doing so isn't necessary. , horizontal stretch bafo 2 2 , phase shift left 1 When a > 1 the graph is stretched vertically (with any zeros of the function is reflected first about the x-axis and then compressed as in the case when 0 < a < 1. Horizontal translation 8 units right (Right 8) Vertical stretch by a factor of 2 Vertical translation 1 unit up (Up 1) 2. Product Business (a - Vertical stretch/compression, b - Horizontal stretch/compression, h - Phase(horizontal shift) & k - Vertical shift) Weblinks shown in class: Graphs of Trig functions: Vertical and Horizontal Shifting Worksheet #3 Microsoft Word - Vertical and Horizontal Shifts Worksheet #3. mathsisfun. = 4 sin x 2. 2 Algebra II Notes Quadratic Functions Unit 3. 45, horizontal shift left 8. The science Conversational presenting. Multiple Transformations Worksheet Functionsf04 A1fn018ws Transformations are ways that a function can be adjusted to create new functions. a. undergo a horizontal stretching or compression. 12b Vertical compression. reflection Transform f(x) with a vertical stretch of 2 and then reflect over the x‐axis. 2 f ( x ) is stretched in the y direction by a factor of 2, and f ( x ) is shrunk in the y direction by a factor of 2 (or stretched by a factor of ). If 0 < C < 1, then f(x) has a vertical SHRINK by a factor of C units. Math Worksheets High School Math based on the topics required for the Regents Exam conducted by NYSED. …Graphing Parent Functions Worksheet Graph each function listed below without the use of a calculator. R 5 DMua OdSe H Gwsi Et6hK AIRnnf8iRnHiut Pek IA bl6gke Ebcr Rat P2 u. Write the rule for g(x). The horizontal stretch can typically be determined from the period of the graph. horizontal with a vertical stretch of 2 and then Linear Transformation Worksheet #1 We found some Images about Vertical And Horizontal Shifts Worksheet Answers: Function Stretch & Compression | Study. Assistance may be required. So, it’s very important that you put these graphs and their equations to memory. Absolute Value—reflected over the x axis and translated down 3. Worksheet 4-3. Just remember: The factor of a stretch/compression is always a number bigger Conclusion. Scales (Stretch/Compress)Vertical and Horizontal Shifts of Quadratic Graphs. Stretching Graphs and Compressing Graphs. where the transformation is a vertical stretch if c > 1 and a vertical shrink if 0 < c < 1. Vertex at (3, 4), horizontally stretched by a factor of 1 4 Vertical Stretching and Compression c · f(x) In this part of the worksheet, you’ll look at another way to modify a function and watch what happens to its graph. View Notes - Transforming_Functions_Worksheet from MATH Principles at Lenape High School. 7. a is vertical stretch/compression |a| > 1 stretches |a| < 1 compresses a < 0 flips the graph upside down b < 0 flips the graph left-right; c is horizontal shift . Name: 1. Worksheet - Stretch and Compression Transformations Worksheet – Vertical and Horizontal Asymptotes – Data Tables Download Download Download 2. write the graph of. 1) y + 3 = Vertical and Horizontal Shifting Worksheet #3 Microsoft Word - Vertical and Horizontal Shifts Worksheet #3. b) The parent function f (x) = x is reflected over the x-axis, stretch horizontally by a factor of 3 and then translated 1 unit left and 4 units down. Additional Resources: Practice Worksheet #1 Practice Worksheet #2 Practice R 5 DMua OdSe H Gwsi Et6hK AIRnnf8iRnHiut Pek IA bl6gke Ebcr Rat P2 u. For y = ax², when 0 < a < 1, we have a vertical compression. Note that unlike translations where there could be a more than one happening at any given time, there can be either a horizontal stretch or a vertical compression but not both at the Score : Printable Math Worksheets @ www. horizontal translation right ___ units horizontal translation left ___ units reflection in the ___ axis vertical stretch dilation of ___ ; vertical shrink Write the equation in standard form for the function that is described by the given characteristics. A point $\,(a,b)\,$ on the graph of $\,y=f(x) 5. _____ Which graph best represents the function f(x) = 2x2 - 2? Parent Function Worksheet 1 Author: HUMBLE ISD Last modified by: Brenda Ray Created Date:Transformation worksheet . Stretching a graph involves introducing a coefficient into the function, whether that coefficient fronts the equation as in y = 3 sin(x) or is acted upon by the trigonometric function, as in y = sin(3x). Vertical and Horizontal Shifting Worksheet #3 Microsoft Word - Vertical and Horizontal Shifts Worksheet #3. The graph of y = 5 1 3x is the graph of y = 1x stretched horizontally by a factor of 1 3. J F fA`lTln jreiwgphxtOsq \rbebsyeurAvqeXdQ. Horizontal Stretching and Compression; Explore interactively the vertical shifting of the graph of a function. Overlay the graph of 3sin(x). Use yourVertical Compression or Stretch: None To find the transformation , compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis , and if there is a vertical stretch. 1-3. 7 _____ x 5 0 7 y 3 7 21 Let g(x) be the indicated combined transformation of f(x) x. “h” = horizontal shift “k” = vertical shift “a” = vertical dilation, contraction, and reflection DESCRIBE THE TRANSFORMATIONS FOR THE GIVEN EXPRESSIONS For parent functions f(x), g(x), or h(x)Rational—vertical stretch by 8 Quadratic—vertical compression by . Absolute Value — vertical shift up 5, horizontal shift right 3. htmlFunction Transformations. horizontal stretch by a factor of 3. Learn vocabulary, terms, and more with flashcards, games, and other study tools. For each of the following graphs, rst describe in words how the function was obtained from the parent function, The letter ‘a’ is assigned for vertical stretch/compression, ‘b’ is assigned for horizontal stretch/compression, ‘c’ is assigned for horizontal translation/shift, and ‘d’ is assigned for vertical shift. vertical and horizontal stretch and compression worksheet +ve)→ Horizontal compression by a factor of 𝟏 . For example, the amplitude of y = f (x) = sin(x) is one. The vertical shrink is 1/2 for every point on this function, so each point on the tangent parent graph is half as tall. Do exercises on p. Jones at AHHS. ) • Person 2: Graph y=Vertical Compression or Stretch: None To find the transformation , compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis , and if there is a vertical stretch. 2 answ. 3. Vertical Stretches To stretch a graph vertically, place a coefficient in front of the function. If [latex]c>1 Vertical and Horizontal Shifting Worksheet #3 Name: _____ Date: _____ 1. We found some Images about Vertical And Horizontal Shifts Worksheet Answers: Transformations & Parent Functions transformations and parent functions 4 Quiz & Worksheet - Function Stretch & Compression | Study. Graphing Transformations Techniques -- Team Project Packet A horizontal compression vertical compression horizontal stretch vertical stretch . = –10 – 3 ; compressed horizontally by a factor of . Learn vocabulary, terms, and Transformation: Vertical or Horizontal Stretch / Compression. com/sets/function-transformations. b. Autor: Sal KhanTHE ABSOLUTE VALUE FUNCTION AND ITS TRANSLATIONSmrssnowsmath. Write the rule for g(x), and graph the function. Figure 1 . Absolute Value — vertical shift up 5, horizontal shift right 3. If c<0 then either the horizontal stretch or compression must be followed by a re ection about the y Vertical Stretch or Compression. Stretch/Compression f(x) → af(x). y = -2 cos _1 x 3 Module 19 969 Lesson 1Determining Sequence of Function Transformations Worksheet – Answers 1. VERTICAL Number outside the parentheses, absolute value bars or radical sign. This video looks at how a and b affect the graph Function stretch and compression will be the subject of these interactive study resources. Vertical Stretching and Shrinking are Reflecting in the y-axis Horizontal Reflecting in the x-axis Vertical Vertical stretching/shrinking Vertical Horizontal stretching/shrinking Horizontal A summary of the results from Examples 1 through 6 are below, along with whether or not each transformation had a vertical or horizontal effect on the graph. 45, horizontal shift left 8. c < 0 shifts to the right c > 0 shifts to the left; d is vertical shift. tes. = 3). 1) a. We will see some example problems foe vertical stretch and compression of the graphs. Then, graph the function and identify its period. horizontal compression with a scale factor of 2. This is part 1 of 2! 1. y=1/3*x^2 for example as being squeezed so that the y-coordinates are 1/3 as far from the x-axis as they were in before (in y=x^2) and also 3 times closer to the x-axis. For y = ax², when 0 < a < 1, we have a vertical compression. Vertical and Horizontal Stretches Another common way that the graphs of trigonometric functions are altered is by stretching the graphs. _____ Quadratic—vertical stretch by 5, horizontal stretch/compress by 8, translate Recognize a function showing a vertical compression Understand what the function log (x / 7) shows Choose a function that shows both a vertical stretch and a horizontal compression I’m currently teaching vertical and horizontal stretches/compressions to my Accelerated 8th grade students. Set and . 13. com Name : Write the transformed function. Horizontal Translation f(x) → f(x – c). 11 Ex. 2 Alg II Notes Unit 3. 3­Transforming Linear Functions. f x x( ) 7 4 2 2 b. Linear — vertical stretch/compression by _____ Graph Transformations - Horizontal And Vertical Graph Stretches and Compressions. The amplitude of y = f (x) = 3 sin(x) is three. doc Author: Joy Chaffee Created Date: Transformations and Parent Functions (Complicated examples) Sketch the following ftnctions: + 51 Solutions: (0, If f (x) is the parent function, af(b(x - c)) + d is the transformed function where (6, 0) 5) (6, a is the b is the c is the d is the "stretch" "compression" 'horizontal shift" "vertical shift" To check your graph, select some points: ©k _2U0V1H7V JKbu_tkac DSaoLfytlwIavrEeZ CL]LxCc. And graph the function. Vertical stretch factor of 2 and vertical translation 1 unit up. Try it! Vertically compress y = 3x by a scale factor of 1/4 Horizontal compressions and stretches the number will be inside touching Video 4: Vertical Stretch and Compression of y = x² For y = a x², when a > 1, we have a vertical stretch. Graphing Horizontal and Vertical Lines Worksheet *AP and SAT 0 < < 1 → Vertical compression by a factor of a. To perform a horizontal compression or stretch on a graph, instead of solving your equation for f(x), you solve it for f(c*x) for stretching or f(x/c) PreCalculus – Parent Graphs & Transformations For problem 1- 6, please give the name of the parent function and describe the transformation Linear—vertical stretch/compression by 2 5 _____ 12. y=(1/2x) Start studying Regular Algebra 2 Exam Horizontal/Vertical stretch/compression rules. horizontal translation 5 units left 3. c) g (x) is a horizontal stretch by a factor of 5 2 d) g (x) is a vertical stretch by a factor of 8 3. Example: 2√(x+1)+1. Linear — vertical stretch/compression by 2 Quadratic — vertical stretch by 5, horizontal shift left 8. It looks at how a and b affect the graph of f(x). [19] A parabola is reflected in the x-axis, translated down 4 Horizontal shrinking and stretching For the next two transformations, why don’t you try graphing them on your own. This series of worksheets requires learners to find the vertical stretch or compression by multiplying the function f(x) by the given factor and the horizontal stretch horizontal relection over the y-‐axis − d) vertical reflection over the x-‐axis and vertical compression bafo. 1-3. Problem. Then graph the Changing the value of a will cause a vertical stretch or compression; changing the value of h will cause a horizontal shift; and changing the value of k will cause a vertical shift. In many functions like the absolute value function, the horizontal compression appears to be a vertical stretch. = 2 + 3 ; stretched vertically by a factor of 5. The result will produce an image graph that Algebra II Notes Quadratic Functions Unit 3. Vertically stretch y = 3x by a scale factor of 2 Simply put the 2 on the outside of 3x like this: y = 2(3x) That’s it???? Yep, that’s it! But what if it is a compression? Same deal but you will see a fraction. Function Transformations: Horizontal and Vertical Stretch and Compression This video explains to graph graph horizontal and vertical stretches and compressions in the form af(b(x-c))+d. Horizontal Stretch of an Exponential Function Horizontal Stretch x y2= c • Another transformation that can be made to the base function is to change the Horizontal Stretch (HS). Show all Give a function f, which of the following represents a horizontal stretch by a factor of 3? (A) . Check Your Answer Math with Ms. y = _1 cos 2 2 x 3. [19] A parabola is reflected in the x-axis, translated down 4 with a horizontal compression by a factor of 1/4, a vertical translation 4 units down, and a reflection across the x-axis a vertical stretch by a factor of 6, and Transformations of Polynomial Functions A polynomial of the form f(x) = a(b(x c))n + d, where a, b,c and d are real constants, and n is a natural number, is a transformation of some power function g(x) = xn. Vertical Stretching and Shrinking …Determining Sequence of Function Transformations Worksheet – Answers 1. The graph of y= f(cx) is the graph of y= f(x) horizontally stretched (respectively compressed) by a factor of 1 c;if 0 <c<1 (respectively c>1). 3 videos. y1. Stretch and Compress Transformations of Explore the horizontal shift of the graph of a function. _____ Quadratic—vertical stretch by 5, horizontal stretch/compress by 8, translate right 2. Root —flipped over the x axis, vertical shift down 2. The vertex is the midpoint between the focus and the directrix. Draw the graphs here. Transformations of Functions S. 6 Graphical Transformations (vertical and horizontal stretches and shrinks) Do Worksheet is a vertical stretch of f(x) by a factor of 3. A combination of horizontal and vertical shifts is a translation of the graph, a combination of horizontal and vertical compression and stretching is a scaling of the graph. Cubic—reflected over the x axis and vertical shift down 2 16. where the transformation is a vertical stretch if c > 1 and a vertical shrink if 0 < c < 1. 1 – 3. j Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Graphing Simple Rational Functions Date_____ Period____ Identify the vertical asymptotes, horizontal asymptote, domain, and range of each. Video 4: Vertical Stretch and Compression of y = x² For y = a x², when a > 1, we have a vertical stretch. The horizontal • The Horizontal Stretch is the SAME as the value multiplied by x in the mapping rule. 8/12/2008 · Horizontal And Vertical Graph Stretches and Compressions Part 1 of 3 Horizontal And Vertical Graph Stretches and Compressions. 6. Vertical Stretch: Adding Exponents Worksheet. Let's begin with a quadratic function. Next overlay the graph of 1 2 sin(x). _____ 12. Graphically, a vertical stretching pulls the graph of away from the y-axis. Graphs MUST be on this worksheet or on graph paper. Linear — vertical stretch/compression by _____ Start studying Regular Algebra 2 Exam Horizontal/Vertical stretch/compression rules. (ii) Sketch an accurate graph of the transformed function. Stretch, Compression, and Reflection y = a0x 0 y = 0bx 0 0a 0 7 1 vertical stretch 0b 0 7 1 horizontal compression (shrink) 0 6 0a 0 6 1 vertical compression (shrink) 0 6 0b 0 6 1 horizontal stretch a 6 0 reflection across x-axis b 6 0 reflection across y-axis Concept Summary Absolute Value Function Family 2-4 Transformations of Absolute Value h result in horizontal translations a result in vertical stretches and compressions (dilations), as well as reflections across the x -axis b result in horizontal stretches and compressions (dilations), as well as reflections across the y -axis #12 - 16 Given the parent function and a description of the transformation, write the equation of the transformed function, f(x). a is –ve → Vertical reflection (reflection in the x-axis). Write the rule for g(x), and graph the Let g(x) be a vertical shift of f(x)=x down 2 units followed by a vertical stretch by a factor of 5. Horizontal Stretching and Compression; Explore interactively the vertical shifting of …Transformations of Functions Name _____ Date _____ Give the name of the parent function and describe the transformation represented. Write the velocity function h for the Moon, and use it to estimate the downward velocity of a landing craft at the end of a bounce 50 ft in height. Why Prezi. To stretch or shrink the graph in the y direction, multiply or divide the output by a constant. Worksheet 1-7 3. Transformations+of+ ! Vertical/Horizontal Stretching/Shrinking usually changes the shape of a graph. this means that we have to modify the x value. I’m currently teaching vertical and horizontal stretches/compressions to my Accelerated 8th grade students. com Print Stretching & Compressing a Function Worksheet. com//horizontal-compression-stretches-6349076Identify Horizontal and Vertical Stretches and Compressions - Function Notation. Note: for a horizontal reflection, the point (x, y) becomes point (-x, y) August 22, 2013 Math Concepts compressing graphs, horizontal compression, horizontal stretching, stretching graphs, vertical compression, vertical stretching Numerist-Shaun If you understand how to shift a curve horizontally or vertically , stretching and shrinking graphs isn’t much different. Powered by Create your own unique website with customizable templates. b is –ve → Horizontal reflection (reflection in the y-axis). _____ Quadratic—vertical stretch by 5, horizontal shift left 8. Sep 5, 2018 PRACTICE (online exercises and printable worksheets) Vertical/Horizontal Stretching/Shrinking usually changes the shape of a graph. …a. The result will produce an image graph that Vertical translation Horizontal translation Vertical stretch or compression Horizontal stretch or compression Reflection f(x) Notation f(x) + k f(x — h) af(x) f(—x) Examples 3 units up 4 units down 2 units right 1 unit left stretch by 6 compression by — stretch by 5 compression by — across x-axis across y-axis log x +3 logx—4 Section 2. Given the parent function and a description of the transformation, write the equation of the transformed function, f(x). Note: for a horizontal reflection, the point (x, y) becomes point (-x, y)Video 4: Combining Vertical Stretch/Compression and Reflection of y = x Worksheet 1-6 2. Which graph best represents the function Horizontal shrinking and stretching For the next two transformations, why don’t you try graphing them on your own. Day 4: Review Day Practice Test #1 Answer Key Practice Test #2 Answer Key Review Homework Answer Key Extra Practice Answer Key Interactive Practice Test . In algebra, this essentially manifests as a vertical or horizontal shift of a function. Vertical and Horizontal Shifts of Quadratic Graphs a) g (x) is a horizontal compression by a factor of 4 9 b) g (x) is a vertical compression by a factor of 4 5. So, every point on the new function is half of its original distance from the y- axis. Alissa Fong You don't have to make a table you can just use these shifting rules the -2 tells you a horizontal shift but it's counter intuitive the +3 tells you the Transformations of the Sine and Cosine Graph – An Exploration. Vertex at (3, 4), horizontally stretched by a factor of 1 4Vertical Stretching and Shrinking of Quadratic Graphs A number (or coefficient) multiplying in front of a function causes a vertical transformation. The lesson Graphing Tools: Vertical and Horizontal Scaling in the Algebra II curriculum gives a thorough discussion of horizontal and vertical stretching and shrinking. (a)Absolute Value { vertical shift up 5, horizontal shift right 3. 3­Transforming Linear Functions. Some of the worksheets displayed are Transformations, Graphical transformations of functions, Transformations of graphs date period, Igcse mathematics transformations transformation matrix, Vertical and horizontal shifts of graphs, Graph the image of the figure using the transformation, Transformations is a constant, is a horizontal stretch or horizontal compression of the function f (x). base function: y = x horizontal shift left 2 → y = x +2 vertical stretch of shrink by a factor of a → y =a x +2 In other words, we may equally view Y2 as a horizontal compression or as a vertical stretch, and Y3 as a horizontal stretch or a vertical compression! This is why linear functions, absolute-value functions, and quadratic functions all are not such great illustrations of the difference between horizontal and vertical dilations. com Print Stretching & Compressing a Function Vertically stretch y = 3x by a scale factor of 2 Simply put the 2 on the outside of 3x like this: y = 2(3x) That’s it???? Yep, that’s it! But what if it is a compression? Same deal but you will see a fraction. p V \MHaEdOel hwniZtyhU HIgnWfliQnnittKeN yParZeScQapl^cRualYuQse. 1 ( ) 5 5 fx x …Transformations of Polynomial Functions A polynomial of the form f(x) = a(b(x c))n + d, where a, b,c and d are real constants, and n is a natural number, is a transformation of some power function g(x) = xn. notebook 10 December 11, 2013 Let g(x) be a horizontal compression of f(x)=2x­1 by a factor of 1/3. Alissa Fong. 2 followed by vertical stretch of the graph of fix) by horizontal compression of the graph of f(x) by a factor of a horizontal stretch by a factor of 3. Describe how the coordinates change when you vertically compress a function by a Vertical Translation f(x) → f(x) + d. 0 < < 1→ Vertical stretch by a factor of 𝟏 . This activity is designed for Algebra 2, PreCalculus, or College Algebra students. d > 0 shifts upward d < 0 shifts downward . A translation can be interpreted as shifting the origin of the coordinate system. 5 or 1. Quadratic—vertical compression by . Thegraphofy = f (x−a) 2. So when the function becomes and , a horizontal stretching of the graph of will occur. b) Horizontal compression by a factor of 7 10, a vertical stretch by a factor of 8 Precalculus Examples. y = -3 sin _1 x 6 4. T m UANlUlJ ArtiTgshPtEsk GrHeLsIeWrNvEeBdQ. August 22, 2013 Math Concepts compressing graphs, this is a vertical stretch graph. _____ 15. Which graph best represents the function f(x) = 2x2 - 2? This produces a vertical stretch, where the $\,y$-values on the graph get multiplied by $\,2\,$. Use the graph of the elementary, or arbitrary, function y = h(x) below. 12. Concept. In the form above: a is a vertical stretch/compression, and possibly a re ection b is a horizontal stretch/compression, and possibly a re Some of the worksheets displayed are Shifting reflecting and stretching graphs, Vertical and horizontal shifts work 3, Graphing exponential functions, Vertex form of parabolas, Graphing by shifting reflecting and dilation, Vertical and horizontal shifts of graphs, Executive functioning across the lifespan older adults, Graphical transformations 2. Search Results for compression - All Grades. Transformation - Compression/Stretch. 1 - Vertical and Horizontal Shifts Translations of a Function and Its Graph A vertical or horizontal shift of the graph of a function is called a translation because it does not change graph, is altered by a vertical stretch or compression. f(x) = | Functions Worksheet2. h indicates a horizontal translation k indicates aReciprocal—vertical stretch by 8 _____ Quadratic—vertical compression by . Vertical and Horizontal shifts of Quadratic Graphs multiplying in front of a function causes a vertical transformation. _____ 3. Transforming the Graphs of Sine and Cosine So this is a vertical compression, this is a vertical stretch. 1. If 0 < b < 1, then the graph will be stretched by 1 b. 1) f (x) = − 4 xTRANSFORMATIONS OF TRANSFORMATIONS NOTES the equation STRETCH/COMPRESSION Number at the beginning of the equation. Basic knowledge of translation such as horizontal shift and vertical shift; reflection, horizontal / vertical stretches and horizontal / vertical compressions are horizontal relection over the y-‐axis − d) vertical reflection over the x-‐axis and vertical compression bafo. If b > 1, then the graph will be compressed by 1 b. with vertical stretch or compression as well as with vertical stretch or compression as well as horizontal and Horizontal: x = a (y - k) 2 + h. Step-by-Step Examples compare the two functions and check to see if there is a horizontal or vertical shift, and if there is a vertical Just as multiplying a function by a constant stretches or shrinks the graph vertically, multiplying the x-value by a constant before applying the function will stretch or shrink the graph horizontally. For y = a x², when 0 < a < 1, we have a vertical compression. 2 Graphing Quadratic Functions Page 3 of 17 8/27/2014 vertical stretch or compression. If b < 0, then there will be combination of a horizontal stretch or compression with a horizontal reflection. , vertical stretch by a factor of 3, right 7 and up 19. Note that unlike translations where there could be a more than one happening at any given time, there can be either a horizontal stretch or a vertical compression but not both at the This Vertical and Horizontal Stretches and Compressions Lesson Plan is suitable for 9th - 11th Grade. Horizontal compression bfo e. Function stretch and compression will be the subject of these interactive study resources. 215 in TextStart studying Regular Algebra 2 Exam Horizontal/Vertical stretch/compression rules. (x,y) → (x, ay). Given the parent function and a description of the transformation, write the equation of the transformed function, f(x). If is positive, the function was translated units right. 8-7 Radical Functions 623 Use the information on the previous page to answer the following. Stretch and Compress Transformations of Functions, Horizontal and Vertical Scaling. p V \MHaEdOel hwniZtyhU HIgnWfliQnnittKeN yParZeScQapl^cRualYuQse. (x,y) → (x+c, y). Section 2: (1) Graph the transformation (2) Label 3 points guaranteed to be on the graph 1. Write the equation for k (x). About the topic "Investigating horizontal stretches compressions and reflections" we have explained the rule that we have to apply to make horizontal stretch, compression and reflection in a function. While horizontal and vertical shifts involve adding constants to the input or to the function itself, a stretch or compression occurs when we multiply the parent function [latex]f\left(x\right)={b}^{x}[/latex] by a constant [latex]|a|>0[/latex]. In the form above: a is a vertical stretch/compression, and possibly a re ection b is a horizontal stretch/compression, and possibly a re This worksheet examines various transformations. Therefore, the horizontal shift is 6 ± 4. parent graphs). Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations . Notes for EER #4 – Graph transformations (vertical & horizontal shifts, vertical stretching & compression, and reflections) of basic functions. e. If a is larger than 1, then the function is vertically stretched by a factor of a. Basic Functions If C > 0, then f(x) has a vertical STRETCH by a factor of C units. Unit 2 Section 2 looks at the transformation of the graphs of exponential functions. Vertical expansion and compression Distributive property Video 3: Vertical Stretch and Compression of y = x ² For y = ax², when a > 1, we have a vertical stretch. Transformations+of+ !Quiz & Worksheet - Function Stretch & Compression Worksheet. Graphing crazy library/parent functions with stretch, flips, and vertical and horizontal shifts horizontal stretch a transformation that stretches a function’s graph horizontally by multiplying the input by a constant 0 < b < 1 odd function a function whose graph is unchanged by combined horizontal and vertical reflection, f (x) = − f (− x), and is symmetric about the origin. Magnifications • Person 1: Graph y= lnx, y= 4lnxand y= ln(4x) (Make special note of where the graph crosses the x-axis. Linear — vertical stretch/compression by _____Determine a Horizontal Stretch or Horizontal Compression. Algebra II Notes Quadratic Functions Unit 3. Product Business vertical shrink by a factor of 4 1 y ()x 3 2 1 4 1 = − + To check your equation, graph it on a graphing calculator using the same window as the given graph and check to see if all the points are the same. 8. In general: Example 3 on pg. If is negative, the function was translated units left. Horizontal Stretch of an Exponential Function Horizontal Stretch x y2= c • Another transformation that can be made to the base function is to change the Horizontal Stretch (HS). Compare the two The Rule for Horizontal Stretches and Compressions: if y = f(x), then y = f(bx) gives a horizontal stretch when 0 < b < 1 and a horizontal compression when b > 1. Product BusinessLinear Transformation Worksheet #1 3. Basic Functions In several sections you will be applying shifts and transformations to these basic functions. mathworksheets4kids. Test questions will cover points of interest like stretching a function vertically and horizontal Horizontal Stretching and Compression of Graphs This applet helps you explore the changes that occur to the graph of a function when its independent variable x is multiplied by a positive constant a (horizontal stretching or compression). If a is negative the parabola opens left |a| = 1 normal width |a| > 1 narrow width (horizontal stretch) |a| < 1 wider width (horizontal shrink) vertex (h, k) axis of symmetry: y = k. e. Cubic—translated left 1 and up 9. ©A [2[0g1x6F SKQustAal hSAoZf`tMw]alrAeT LLELvCN. Sheet 1. When you multiply a function by a positive a you will be performing either a vertical compression or vertical stretching of the graph. Stretch Transformation. Horizontal translation 7 units left (Left 7) Reflection over the x-axis* Vertical compression by a factor of 4* Vertical translation 5 units down (Down 5) 1. k: horizontal stretch/compression The graph of g(x) = f(kx) is a horizontal stretch or compression of the graph of f(x) by a factor of Note: a vertical stretch or compression means that distance from the y-axis of each point of the parent function changes by a factor of 1/k. Describing a transformation with vertical and horizontal Autor: patrickJMTVizualizări: 188 miiHorizontal Compression/Stretches by mathispower4u https://www. Horizontal translation 7 units left (Left 7) Reflection over the x-axis* Vertical compression by a factor of 4* Vertical translation 5 units down (Down 5)Sal walks through several examples of how to write g(x) implicitly in terms of f(x) when g(x) is a shift or a reflection of f(x). If a is Autor: Mr. Vertical and Horizontal Shrink or stretch the parent graph. b) The parent function f (x) = x is reflected over the x-axis, stretch horizontally by a factor of 3 and then translated 1 unit left and 4 units down. Example 1 Vertical and Horizontal Shifting Worksheet #3 Microsoft Word - Vertical and Horizontal Shifts Worksheet #3. Transformation: Vertical or Horizontal Stretch / Compression. Replace every $\,x\,$ by $\,5x\,$, giving the new equation [beautiful math coming please be patient] $\,y=2{\text{e}}^{5x}\,$. 2 Alg II Notes Unit 3. 4—Parent Functions & Transformations. Resource ID#: 46614 Primary Type: Lesson Plan. …Choose from 500 different sets of quadratic functions transformations flashcards on Quizlet. To obtain the graph of y =cf (x): stretch the graph of y = f (x)vertically by a factor of c 1 f x c y = : compress the graph of y = f (x)vertically by a factor of c dilation of ___ ; vertical shrink Write the equation in standard form for the function that is described by the given characteristics. With tangent graphs, it is often necessary to determine a vertical stretch using a point on the graph. f(x) 1. Vertex at (4, 2), opening left with a horizontal stretch by a factor of 3. vertical translation down 2 units followed by a horizontal compression by a factor of 2 5 _____ 7. If the constant is grouped with the x, then it is a horizontal shift, otherwise it is a vertical shift. 6 Graphical Transformations functions that map real numbers to real numbers Rigid transformations: size and shape are unchanged (translations, reflections, or any combination of these) Non-rigid transformations: shape distorted (vertical and horizontal stretches and shrinks) Do Worksheet Do Exploration #1 on Pg. . 138 Why Prezi. The kinds of changes that we will be making to our logarithmic functions are horizontal and vertical stretching and compression. Students write equations of transformed parabolas and absolute value equations given a stretch/shrink factor and vertical horizontal shift. vertical compressionThe letter ‘a’ is assigned for vertical stretch/compression, ‘b’ is assigned for horizontal stretch/compression, ‘c’ is assigned for horizontal translation/shift, and ‘d’ is assigned for vertical shift. Vertical and Horizontal Shifts of Graphs Graphs of Some Basic Functions: SECTION 1. The following table summarizes the graph transformations discussed in this worksheet. Horizontal Translation . Stretch Compression 𝑛>1 0<𝑛<1 Left Right Up Down − × × + − + − How does the vertical stretch, vertical compression, or vertical reflection of exponential and logarithmic functions compare to the same transformations of other functions, such as quadratic, square root, or rational functions? Interactive popup. Vertical stretch bfo e. Score : Printable Math Worksheets @ www. With the tangent function, like the sine and cosine functions, horizontal stretches/compressions are distinct from vertical stretches/compressions. Vertex at (3, 4), horizontally stretched by a factor of 1 4 PreCalculus – Parent Graphs & Transformations Linear—vertical stretch/compression by 2 Parent Function Worksheet 1 Compression of the graph means squeezing the given graph towards the axis. 38 - #1, #3, #4 to 9. Practice Describe the transformation of the graph of the parent function f ( x ) = 1 over x 1 x to the graph of the rational function f ( x ) = 3 over x 3 x . +ve)→ Horizontal compression by a factor of 𝟏 . The downward velocity function for the Moon is a horizontal stretch of f by a factor of about __25 4. What is f(3)?______ Remember that this is actually corresponding to a point on the graph Function Transformations: Horizontal and Vertical Stretch and Compression This video explains to graph graph horizontal and vertical stretches and compressions in the form af(b(x-c))+d. Vertical translation Horizontal translation Vertical stretch or compression Horizontal stretch or compression Reflection f(x) Notation f(x) + k f(x — h) af(x) f(—x) Examples 3 units up 4 units down 2 units right 1 unit left stretch by 6 compression by — stretch by 5 compression by — across x-axis across y-axis log x +3 logx—4 Horizontal Stretch of an Exponential Function Horizontal Stretch x y2= c • Another transformation that can be made to the base function is to change the Horizontal Stretch (HS). Shifts are added/subtracted to the x or f(x) components. mathworksheets4kids. The key concepts are repeated here. Collectively these are often called transformations and if we understand them they can often be used to allow us to quickly graph some fairly complicated functions. com/Chapter 2 · Fișier PDFVertical translations: Translation up k units Translation down k units Horizontal translations: Translation right h units Translation left h units Combined horizontal and vertical Reflection in x-axis Stretch Shrink Shrink/stretch with reflection Vertex form of Absolute Value Function THE ABSOLUTE VALUE FUNCTION AND ITS TRANSLATIONS:Vertical and horizontal shifts can be combined into one expression. Vertical. The general formula is given as well as a few concrete examples. Additional Resources: Practice Worksheet #1 Practice Worksheet #2 Practice Rational—vertical stretch by 8 Quadratic—vertical compression by . August 22, 2013 Math Concepts compressing graphs, horizontal compression, horizontal stretching, stretching graphs, vertical compression, vertical stretching Numerist-Shaun If you understand how to shift a curve horizontally or vertically , stretching and shrinking graphs isn’t much different. Horizontal translation 4 units right. is a vertical stretch of f(x) by a factor of 3. Please sketch each graph on its own coordinate plane. la vertical stretch or compression factor a reflection across the x-axis h horizontal translation 1b —(x—h + k k vertical translation b I —+ horizontal stretch or compression …Exploration - Horizontal and Vertical Stretch and Compression: 2. _____ 4. gives a thorough discussion of horizontal and vertical stretching and shrinking. horizontal compression. Vertical stretch Horizontal compression Horizontal stretch Grade 9 Waves and Sound Vibrations cause compressions and Rarefactions . Figure 2 Vertical Stretch, that has been stretched vertically with respect to the base function, Vertical Shrink, that has been compressed vertically with respect to …Lesson 3: Vertical Stretch "y = ax²" (4. HORIZONTAL Number inside parentheses, absolute value bars or under the radical sign. 1 Transform y k(x) by stretching it vertically by a factor of 2. The exercises in this lesson duplicate those in Graphing Tools: Vertical This is called a horizontal stretch. a horizontal stretch is given by the equation [latex]y = f(cx)[/latex]. j Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Graphing Simple Rational Functions Date_____ Period____ Identify the vertical asymptotes, horizontal asymptote, domain, and range of each. 7 min . Some of the worksheets displayed are Transformations, Graphical transformations of functions, Transformations of graphs date period, Igcse mathematics transformations transformation matrix, Vertical and horizontal shifts of graphs, Graph the image of the figure using the transformation, Transformations Intro to Graphing Transformations Graphing crazy library/parent functions with stretch, flips, and vertical and horizontal shifts is pretty confusing for most students. notebook 17 December 11, 2013 Sep 2­8:09 PM Stretching and Compressing Linear Functions Let g(x) be a horizontal compression of f(x)=2x­1 by a factor of 1/3. Given a function `f`, multiplication by values of `c` other than `+- 1` results in graphs of functions that are stretched or compressed (depending on the magnitude of `c`). The lesson Graphing Tools: Vertical and Horizontal Scaling in the Algebra II This quiz and worksheet will help you discover what you know about function Which of the following represents one way to stretch the function vertically?Videos, worksheets, solutions, and activities to help PreCalculus students learn Function Transformations: Horizontal and Vertical Stretch and CompressionWorksheet 1. Stretching and Compressing Functions or Graphs Related Topics: More Lessons for High School Regents Exam Function Transformations: Horizontal and Vertical Stretches and Compressions This video explains how to graph horizontal and vertical stretches and compressions in the form a×f(b(x - c)) + d. We can flip it upside down by multiplying the whole function by −1: 12. with a horizontal compression by a factor of 1/4, a vertical translation 4 units down, and a reflection across the x-axis a vertical stretch by a factor of 6, and Vertical and Horizontal Stretching and Compressing. (b)Linear { vertical stretch/compression by 2=5. compression. Linear---vertical stretch of 8 and translated up 2. 1 Horizontal Translations Ifwebeginwiththeformulay = f (x) and we replace x with x−a where a is a constant, then we get the formula y = f (x−a). Vertical Line Test for a Function A vertical line can intersect the graph of a function in at most one point, or using an alternate form, If any vertical line intersects the graph at more than one point, then the graph is NOT the graph of a function. f) g (x) is a reflection across the y-axis. The result will produce an image graph that Rational—vertical stretch by 8 Quadratic—vertical compression by . Example for vertical stretch: Graph the following function and its vertical stretch. Notes for EER #4 – Graph transformations (vertical & horizontal shifts, vertical stretching & compression, and reflections) of basic functions. That is, h = 1. Worksheet by Kuta Software LLC compression/stretch, vertical shifts and horizontal shifts). 138 2. 5-1 Using Transformations to Graph Quadratic Functions 315 In Chapters 2 and 3, you studied linear functions 5-1 Using Transformations to Graph Quadratic Functions 317 Reflections, Stretches, and Compressions of Quadratic Functions Horizontal Stretch/Compression by aThe first example creates a vertical stretch, the second a horizontal stretch. On your calculator graph sin(x) on the interval −10 ≤ x ≤ 10. Let k (x) be the indicated transformations of hx x()=2. Vertical Translation. _____ Quadratic—vertical stretch by 5, horizontal stretch/compress by 8, translate Video 3: Vertical Stretch and Compression of y = x ² For y = ax², when a > 1, we have a vertical stretch. The Rule for Horizontal Stretches and Compressions: if y = f(x), then y = f(bx) gives a horizontal stretch when 0 < b < 1 and a horizontal compression when b > 1. Parent Function Worksheet 1 Author: Horizontal Stretching and Compression of Graphs This applet helps you explore the changes that occur to the graph of a function when its independent variable x is multiplied by a positive constant a (horizontal stretching or compression). com. , horizontal stretch bafo 2 2 , phase shift left 1 Combined Transformation Worksheet. a) Horizontal stretch by a factor of 4 3, vertical compression by a factor of 2 5, and a vertical translation 8 up. doc Author: Joy Chaffee Created Date: Day 3: Horizontal and Vertical Shifts, Reflections and Steepness Lesson Notes Answer Key Homework Answer Key . doc Author: Joy Chaffee Created Date: Horizontal movment · y = (x + 3)2 à translates 3 units left · y = (x – 3)2 à translates 3 units right Compression/Stretch · y = 1x2 à vertically compressed by a factor of 1 2 2 · y = 2x2 à vertically stretched by a factor if 2 Reflection Page 1, functions transformations stretch compression reflection vertical shift end point, Brightstorm. When you increase b you get a horizontal compression d) a vertical expansion by a factor of 2 and horizontal compression by a factor of 1 4 **These questions are from the Mathematics 11 textbook, published by McGraw-Hill Ryerson in 2001** List the properties these equations have if they are symmetric to the Vertical Stretching and Compression: Example of Horizontal Stretching and Compression: Transformations and Parent Functions (Complicated examples) Sketch the following ftnctions: + 51 Solutions: (0, If f (x) is the parent function, af(b(x - c)) + d is the transformed function where (6, 0) 5) (6, a is the b is the c is the d is the "stretch" "compression" 'horizontal shift" "vertical shift" To check your graph, select some points: Using Transformations to Graph Quadratic Functions vertical compression of f Vertical stretch by : 4 3 4 a 3. What about negatives? it is a horizontal stretch by a factor of 2. The horizontal stretch affects the graph by stretching (or compressing) the graph horizontally. Show Remarks/Examples Worksheet, Student Center Activity