(Part 3). You may be asked to write or graph a function with multiple transformations. Save. f (x). 42% average accuracy. Vertical Stretches To stretch a graph vertically, place a coefficient in front of the function. I then checked my textbook and the definition for stretch and compression are the same but it added on that a horizontal stretch is the distance from the y-axis of every point growing by a scale factor greater than 1, while a horizontal compression is the distance from the y-axis of every point shrinking by a scale factor between 0 and 1. Make predictions for what will happen. Any surprising behavior and vertical horizontal and compression using advanced terms that progresses through each of horizontal changes. Start studying Horizontal and Vertical Stretches and Compressions. What if you wanted to do a horizontal shift of f(x) = 3x left 6 units followed by a horizontal stretch by a factor of 4? the rubber band, the interior gets skinnier or the edges get closer Horizontal translation. Q. Vertical compression is a f(x) when a is... answer choices . Given the function for the Y screen y1(x) 0.1(x3 9x2) Use window -10 lt x lt 10 and -20 lt y lt 20 ; Now do the transformation ; y2(x) y1(.5x) y3(x) y1(3x) Set the styles different. Copyright © 2005, 2020 - OnlineMathLearning.com. Subsection Exercises 1 Describing Shifts and Reflections To create a horizontal stretch, compression, or reflection, you need to multiply by b every time x shows up in the function. Graphing a Horizontal Compression. after a vertical compression by a factor of , a horizontal stretch by a factor of , and a reflection in the y-axis 1 0.5, or 2 1 4 y x3 6x y 1 4 ca 1 2 xb 3 6a 1 2 xbd 1 2 1 4 y3 1 4 ca 1 2 xb 3 6a 1 2 x 6x xbd ©P DO NOT COPY. As you may have notice by now through our examples, a horizontal stretch or compression will never change the \(y\) intercepts. Write a formula to represent the function. In respect to this, what is a horizontal stretch or compression? Horizontal Stretches and Compressions. a is greater than 0. a is less than 0. a is greater than 1. a is a fraction/decimal. Horizontal compressions occurs when the function’s base graph is shrunk along the x-axis and consequent, away from the y-axis. Mathematics. Lesson 5.4; 2 Manipulating a Function. It looks at how a and b affect the graph of f(x). This type of Edit. Let y = f(x) be a function. gets bigger or the edges get farther apart. Is a vertical compression the same as a horizontal stretch? Set g(x) = f (bx) g ( x) = f ( b x) where b> 1 … y = f(x - c), will shift f(x) right c units. Isn’t it interesting that by inspecting coefficients, we can either stretch or compress a function’s graph? Function stretch and compression will be the subject of these interactive study resources. 10th - 12th grade. We can graph this math Embedded content, if any, are copyrights of their respective owners. 3 Manipulating a Function. Now, based on this can you make generalizations about horizontal stretch or a vertical compression but not both at the same time. This video explains to graph graph horizontal and vertical stretches and compressions in the If the constant is between 0 and 1, we get a horizontal stretch; if the constant is greater than 1, we get a horizontal compression of the function. Write the rule for g(x), and graph the function. Which equation has a horizontal compression by a factor of 2 and shifts up 4? b = 2, Indicates a horizontal compression by a factor of . Edit. 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. Tags: Question 10 . The general formula is given as well as a few concrete examples. When one compresses Vertical stretch/compression. More Pre-Calculus Lessons. and reflections across the x and y axes. (Remember that horizontal stretch and compression are opposite of vertical stretch and compression!) Though both of the given examples result in stretches of the graph of y = sin(x), they are stretches of a certain sort. This video explains to graph graph horizontal and vertical translation in the form af(b(x-c))+d. Note : Stretch and expansion mean the same thing. If is negative, the function was translated units left. What is a horizontal stretch or compression? b > 1. For example, if we begin by graphing the parent function f (x)= 2x f ( x) = 2 x, we can then graph the stretch, using a =3 a = … Horizontal Stretch and Horizontal Compression y = f(bx), b > 1, will compress the graph f(x) horizontally. When one compresses the rubber band, the interior gets fatter or the edges get farther apart. 60 seconds . Horizontal Compression and Stretch DRAFT. math transformation is a horizontal compression when b is greater than one. form af(b(x-c))+d. These lessons with videos and examples help Pre-Calculus students learn about horizontal and vertical Let y = f(x) be a function. In the above function, if we want to do horizontal expansion or compression by a factor of "k", at every where of the function, "x" co-ordinate has to be multiplied by the factor "k". C > 1 compresses it; 0 < C < 1 stretches it; Note that (unlike for the y-direction), bigger values cause more compression. horizontal stretches and compressions. Related Pages Which Other important 21 times. … A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis. handling multiple transformations. Please describe the transformations in words, for example, if there is horizontal stretching, horizontal compression, verticle stretching, verticle compression, horizontal shift, and/or verticle shift. Horizontal Stretching and Shrinking If c is multiplied to the variable of the function then the graph of the function will undergo a horizontal stretching or compression. 0. In the above function, if we want to do horizontal expansion or compression by a factor of "k", at every where of the function, "x" co-ordinate has to be multiplied by the factor "k". If you would like a little more help, 3 Horizontal Shift y = f(x + c), will shift f(x) left c units. Parent Functions And Their Graphs That's horizontal stretching and compression. It looks at how c and d affect the graph of f(x). The lesson Graphing Tools: Vertical and Horizontal Scaling in the Algebra II curriculum gives a thorough discussion of horizontal and vertical stretching and shrinking. Write a formula to represent the function. You can change the base function \(f(x)\) using the input box and see many different stretches/compressions of \(f(x)\) by moving around the \(a\) slider. 1st: translate, 2nd: stretch 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 f (x) = bx f ( x) = b x by a constant |a|> 0 | a | > 0. 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. This video looks at how a and b affect the graph of f(x). 0. problem solver below to practice various math topics. (you can use f(x)=x^2 as an example) - horizontal stretch by a factor of 2 - horizontal stretch by a factor of 1/2 - horizontal compression by a factor of 2 - horizontal compression by a factor of 1/2 I have a test tomorrow so any help is appreciated. We welcome your feedback, comments and questions about this site or page. Title: Horizontal Stretches and Compression 1 Horizontal Stretches and Compression.