vertical and horizontal stretch and compression

y = x 2. (that is, transformations that change the $\,y$-values of the points), The $\,y$-values are being multiplied by a number greater than $\,1\,$, so they move farther from the $\,x$-axis. Genuinely has helped me as a student understand the problems when I can't understand them in class. Horizontal Stretch and Compression. These occur when b is replaced by any real number. For vertical stretch and compression, multiply the function by a scale factor, a. Compare the two graphs below. Write a formula to represent the function. For the stretched function, the y-value at x = 0 is bigger than it is for the original function. Lastly, let's observe the translations done on p (x). That's horizontal stretching and compression.Let's look at horizontal stretching and compression the same way, starting with the pictures and then moving on to the actual math.Horizontal stretching means that you need a greater x -value to get any given y -value as an output of the function. A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis. Now examine the behavior of a cosine function under a vertical stretch transformation. This tends to make the graph flatter, and is called a vertical shrink. Vertical Stretches and Compressions. To determine what the math problem is, you will need to take a close look at the information given and use your problem-solving skills. With a little effort, anyone can learn to solve mathematical problems. Work on the task that is enjoyable to you. (MAX is 93; there are 93 different problem types. Create a table for the function [latex]g\left(x\right)=\frac{1}{2}f\left(x\right)[/latex]. When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. What is vertically compressed? Now, examine the graph below of f(x)=cos(x) which has been stretched by the transformation g(x)=f(0.5x). Each output value is divided in half, so the graph is half the original height. . For example, look at the graph of a stretched and compressed function. What is the relationship between tightness and weak convergence? Again, that's a little counterintuitive, but think about the example where you multiplied x by 1/2 so the x-value needed to get the same y-value would be 10 instead of 5. Try refreshing the page, or contact customer support. If the graph is horizontally stretched, it will require larger x-values to map to the same y-values as the original function. An important consequence of this is that horizontally compressing a graph does not change the minimum or maximum y-value of the graph. Sketch a graph of this population. If you continue to use this site we will assume that you are happy with it. In this lesson, you learned about stretching and compressing functions, vertically and horizontally. If [latex]b<0[/latex], then there will be combination of a horizontal stretch or compression with a horizontal reflection. This is also shown on the graph. For example, say that in the original function, you plugged in 5 for x and got out 10 for y. Learn how to evaluate between two transformation functions to determine whether the compression (shrink) or decompression (stretch) was horizontal or vertical Parent Function Overview & Examples | What is a Parent Function? In the case of above, the period of the function is . horizontal stretch; x x -values are doubled; points get farther away. We welcome your feedback, comments and questions about this site or page. 0 times. g (x) = (1/2) x2. . Learn how to determine the difference between a vertical stretch or a vertical compression, and the effect it has on the graph. Find the equation of the parabola formed by stretching y = x2 vertically by a factor of two. How do you tell if a graph is stretched or compressed? Note that unlike translations where there could be a more than one happening at any given time, there can be either a vertical stretch or a vertical compression but not both at the same time. $\,y = 3f(x)\,$, the $\,3\,$ is on the outside; That's what stretching and compression actually look like. Horizontal And Vertical Graph Stretches And Compressions. A point $\,(a,b)\,$ on the graph of $\,y=f(x)\,$ moves to a point $\,(\frac{a}{k},b)\,$ on the graph of. On the graph of a function, the F(x), or output values of the function, are plotted on the y-axis. Write a formula for the toolkit square root function horizontally stretched by a factor of 3. A General Note: Vertical Stretches and Compressions. problem and check your answer with the step-by-step explanations. x). vertical stretch wrapper. Clarify math tasks. If a > 1 \displaystyle a>1 a>1, then the graph will be stretched. Vertical Shifts Horizontal Shifts Reflections Vertical Stretches or Compressions Combining Transformations of Exponential Functions Construct an Exponential Equation from a Description Exponent Properties Key Concepts Learning Objectives Graph exponential functions and their transformations. Hence, we have the g (x) graph just by transforming its parent function, y = sin x. $\,y=f(x)\,$ and reflections across the x and y axes. To determine what the math problem is, you will need to take a close look at the information given and use your problem-solving skills. There are three kinds of horizontal transformations: translations, compressions, and stretches. This is a transformation involving $\,x\,$; it is counter-intuitive. Just enter it above. Writing and describing algebraic representations according to. A function [latex]f\left(x\right)[/latex] is given below. Replacing every $\,x\,$ by $\,\frac{x}{3}\,$ in the equation causes the $\,x$-values on the graph to be multiplied by $\,3\,$. This will allow the students to see exactly were they are filling out information. Compared to the parent function, f(x) = x2, which of the following is the equation of the function after a vertical stretch by a factor of 3? In a horizontal compression, the y intercept is unchanged. See how the maximum y-value is the same for all the functions, but for the stretched function, the corresponding x-value is bigger. This is how you get a higher y-value for any given value of x. Use an online graphing tool to check your work. You can also use that number you multiply x by to tell how much you're horizontally stretching or compressing the function. Doing homework can help you learn and understand the material covered in class. Make a table and a graph of the function 1 g x f x 2. x fx 3 0 2 2 1 0 0 1 0 2 3 1 gx If f In general, if y = F(x) is the original function, then you can vertically stretch or compress that function by multiplying it by some number a: If a > 1, then aF(x) is stretched vertically by a factor of a. Make sure you see the difference between (say) Look no further than Wolfram. Now let's look at what kinds of changes to the equation of the function map onto those changes in the graph. GetStudy is an educational website that provides students with information on how to study for their classes. If you need an answer fast, you can always count on Google. That's what stretching and compression actually look like. Multiply all of the output values by [latex]a[/latex]. *It's 1/b because when a stretch or compression is in the brackets it uses the reciprocal aka one over that number. Related Pages ), HORIZONTAL AND VERTICAL STRETCHING/SHRINKING. In math terms, you can stretch or compress a function horizontally by multiplying x by some number before any other operations. Explain how to indetify a horizontal stretch or shrink and a vertical stretch or shrink. Vertical Stretches and Compressions When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. Figure %: The sine curve is stretched vertically when multiplied by a coefficient. *It's the opposite sign because it's in the brackets. Vertical Shift Graph & Examples | How to Shift a Graph, Domain & Range of Composite Functions | Overview & Examples. Let g(x) be a function which represents f(x) after an horizontal stretch by a factor of k. where, k > 1. There are plenty of resources and people who can help you out. Which function represents a horizontal compression? You can see this on the graph. Instead, that value is reached faster than it would be in the original graph since a smaller x-value will yield the same y-value. [latex]g\left(x\right)=\sqrt{\frac{1}{3}x}[/latex]. The key concepts are repeated here. This is due to the fact that a compressed function requires smaller values of x to obtain the same y-value as the uncompressed function. In fact, the period repeats twice as often as that of the original function. Just keep at it and you'll eventually get it. and Here is the thought process you should use when you are given the graph of $\,y=f(x)\,$. 2 If 0 < b< 1 0 < b < 1, then the graph will be stretched by 1 b 1 b. No matter what you're working on, Get Tasks can help you get it done. The $\,y$-values are being multiplied by a number between $\,0\,$ and $\,1\,$, so they move closer to the $\,x$-axis. Holt McDougal Algebra 2: Online Textbook Help, Holt McDougal Algebra 2 Chapter 1: Foundations for Functions, Psychological Research & Experimental Design, All Teacher Certification Test Prep Courses, Cardinality & Types of Subsets (Infinite, Finite, Equal, Empty), How to Write Sets Using Set Builder Notation, Introduction to Groups and Sets in Algebra, The Commutative Property: Definition and Examples, Addition and Subtraction Using Radical Notation, Translating Words to Algebraic Expressions, Combining Like Terms in Algebraic Expressions, Simplifying and Solving Exponential Expressions. The graph of [latex]y={\left(2x\right)}^{2}[/latex] is a horizontal compression of the graph of the function [latex]y={x}^{2}[/latex] by a factor of 2. Multiply all range values by [latex]a[/latex]. a function whose graph is unchanged by combined horizontal and vertical reflection, \displaystyle f\left (x\right)=-f\left (-x\right), f (x) = f (x), and is symmetric about the origin. The graphis a transformation of the toolkit function [latex]f\left(x\right)={x}^{3}[/latex]. a transformation that shifts a function's graph left or right by adding a positive or negative constant to the input. Length: 5,400 mm. Embedded content, if any, are copyrights of their respective owners. Width: 5,000 mm. It is used to solve problems. How do you possibly make that happen? Suppose a scientist is comparing a population of fruit flies to a population that progresses through its lifespan twice as fast as the original population. This moves the points closer to the $\,x$-axis, which tends to make the graph flatter. Need help with math homework? For example, the function is a constant function with respect to its input variable, x. We use cookies to ensure that we give you the best experience on our website. However, with a little bit of practice, anyone can learn to solve them. $\,y = f(3x)\,$! Now we consider changes to the inside of a function. It looks at how c and d affect the graph of f(x). Instead, it increases the output value of the function. Horizontal and Vertical Stretching/Shrinking. You must multiply the previous $\,y$-values by $\frac 14\,$. When do you use compression and stretches in graph function? Video quote: By a factor of a notice if we look at y equals f of X here in blue y equals 2 times f of X is a vertical stretch and if we graph y equals 0.5 times f of X.We have a vertical compression. The following table gives a summary of the Transformation Rules for Graphs. Horizontal stretches and compressions can be a little bit hard to visualize, but they also have a small vertical component when looking at the graph. On this exercise, you will not key in your answer. In the function f(x), to do horizontal stretch by a factor of k, at every where of the function, x co-ordinate has to be multiplied by k. The graph of g(x) can be obtained by stretching the graph of f(x) horizontally by the factor k. Note : shown in Figure259, and Figure260. To vertically compress a function, multiply the entire function by some number less than 1. Adding a constant to shifts the graph units to the right if is positive, and to the . I'm not sure what the question is, but I'll try my best to answer it. We do the same for the other values to produce this table. [beautiful math coming please be patient] For those who struggle with math, equations can seem like an impossible task. 2) I have constantly had trouble with the difference between horizontal and vertical compression of functions, their identification, and how their notation works. 2. How do you know if a stretch is horizontal or vertical? A function [latex]f[/latex] is given in the table below. For example, if you multiply the function by 2, then each new y-value is twice as high. 100% recommend. Create a table for the function [latex]g\left(x\right)=f\left(\frac{1}{2}x\right)[/latex]. If f (x) is the parent function, then. Based on that, it appears that the outputs of [latex]g[/latex] are [latex]\frac{1}{4}[/latex] the outputs of the function [latex]f[/latex] because [latex]g\left(2\right)=\frac{1}{4}f\left(2\right)[/latex]. You can always count on our 24/7 customer support to be there for you when you need it. How to Market Your Business with Webinars? If a graph is horizontally compressed, the transformed function will require smaller x-values to map to the same y-values as the original function. We will compare each to the graph of y = x2. Vertical Stretches and Compressions. 2. Multiply the previous $\,y\,$-values by $\,k\,$, giving the new equation Vertical stretching means the function is stretched out vertically, so its taller. Further, if (x,y) is a point on. 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. How can you tell if a graph is horizontal or vertical? This is basically saying that whatever you would ordinarily get out of the function as a y-value, take that and multiply it by 2 or 3 or 4 to get the new, higher y-value. See how we can sketch and determine image points. 6 When do you use compression and stretches in graph function? Vertical/Horizontal Stretching/Shrinking usually changes the shape of a graph. In general, a horizontal stretch is given by the equation y=f(cx) y = f ( c x ) . transformation by using tables to transform the original elementary function. Now it's time to get into the math of how we can change the function to stretch or compress the graph. I'm great at math and I love helping people, so this is the perfect gig for me! This video explains to graph graph horizontal and vertical stretches and compressions in the Divide x-coordinates (x, y) becomes (x/k, y). Horizontal compression means that you need a smaller x-value to get any given y-value. 233 lessons. Look at the compressed function: the maximum y-value is the same, but the corresponding x-value is smaller. I can help you clear up any math tasks you may have. To solve a math equation, you need to find the value of the variable that makes the equation true. By stretching on four sides of film roll, the wrapper covers film . This results in the graph being pulled outward but retaining. Note that the period of f(x)=cos(x) remains unchanged; however, the minimum and maximum values for y have been halved. I'm trying to figure out this mathematic question and I could really use some help. 5 When do you get a stretch and a compression? Has has also been a STEM tutor for 8 years. The x-values for the function will remain the same, but the corresponding y-values will increase by a factor of c. This also means that any x-intercepts in the original function will be retained after vertical compression. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression. Learn about horizontal compression and stretch. 9th - 12th grade. That's great, but how do you know how much you're stretching or compressing the function? [latex]\begin{align}&R\left(1\right)=P\left(2\right), \\ &R\left(2\right)=P\left(4\right),\text{ and in general,} \\ &R\left(t\right)=P\left(2t\right). causes the $\,x$-values in the graph to be DIVIDED by $\,3$. You stretched your function by 1/(1/2), which is just 2. This causes the $\,x$-values on the graph to be DIVIDED by $\,k\,$, which moves the points closer to the $\,y$-axis. Identify the vertical and horizontal shifts from the formula. Vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1. Explain: a. Stretching/shrinking: cf(x) and f(cx) stretches or compresses f(x) horizontally or vertically. How can you stretch and compress a function? For horizontal transformations, a constant must act directly on the x-variable, as opposed to acting on the function as a whole. A scientist is comparing this population to another population, [latex]Q[/latex], whose growth follows the same pattern, but is twice as large. Note that the effect on the graph is a horizontal compression where all input values are half of their original distance from the vertical axis. Notice that the vertical stretch and compression are the extremes. Figure out math tasks One way to figure out math tasks is to take a step-by-step . But, try thinking about it this way. This seems really weird and counterintuitive, because stretching makes things bigger, so why would you multiply x by a fraction to horizontally stretch the function? 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. Horizontal Compression and Stretch DRAFT. We provide quick and easy solutions to all your homework problems. The best teachers are the ones who care about their students and go above and beyond to help them succeed. To scale or stretch vertically by a factor of c, replace y = f(x) with y = cf(x). How can we locate these desired points $\,\bigl(x,f(3x)\bigr)\,$? a is for vertical stretch/compression and reflecting across the x-axis. 16-week Lesson 21 (8-week Lesson 17) Vertical and Horizontal Stretching and Compressing 3 right, In this transformation the outputs are being multiplied by a factor of 2 to stretch the original graph vertically Since the inputs of the graphs were not changed, the graphs still looks the same horizontally. In this lesson, values where c<0 have been omitted because they produce a reflection in addition to a horizontal transformation. Vertical compressions occur when a function is multiplied by a rational scale factor. If you're struggling to clear up a math problem, don't give up! and multiplying the $\,y$-values by $\,\frac13\,$. When trying to determine a vertical stretch or shift, it is helpful to look for a point on the graph that is relatively clear. Relate the function [latex]g\left(x\right)[/latex] to [latex]f\left(x\right)[/latex]. Transform the function by 2 in x-direction stretch : Replace every x by Stretched function Simplify the new function: : | Extract from the fraction | Solve with the power laws : equals | Extract from the fraction And if I want to move another function? 5.4 - Horizontal Stretches and Compressions Formula for Horizontal Stretch or Compression In general: 1 Example 1 on pg. Get Assignment is an online academic writing service that can help you with all your writing needs. Notice how this transformation has preserved the minimum and maximum y-values of the original function. The most conventional representation of a graph uses the variable x to represent the horizontal axis, and the y variable to represent the vertical axis. Each change has a specific effect that can be seen graphically. More Pre-Calculus Lessons. When a compression occurs, the image is smaller than the original mathematical object. Thats what stretching and compression actually look like. The graph belowshows a function multiplied by constant factors 2 and 0.5 and the resulting vertical stretch and compression. 447 Tutors. As compression force is applied to the spring, the springs physical shape becomes compacted. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression. In other words, this new population, [latex]R[/latex], will progress in 1 hour the same amount as the original population does in 2 hours, and in 2 hours, it will progress as much as the original population does in 4 hours. How do you know if its a stretch or shrink? Stretch hood wrapper is a high efficiency solution to handle integrated pallet packaging. In this case, however, the function reaches the min/max y-values slower than the original function, since larger and larger values of x are required to reach the same y-values. Vertical Stretch or Compression of a Quadratic Function. $\,y = f(x)\,$ Practice examples with stretching and compressing graphs. 1 What is vertical and horizontal stretch and compression? Height: 4,200 mm. Once you have determined what the problem is, you can begin to work on finding the solution. dilates f (x) vertically by a factor of "a". However, in this case, it can be noted that the period of the function has been increased. How to graph horizontal and vertical translations? To stretch a graph vertically, place a coefficient in front of the function. 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. Easy to learn. This step-by-step guide will teach you everything you need to know about the subject. The original function looks like. The best way to do great work is to find something that you're passionate about. Looking for help with your calculations? When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original. Notice that the effect on the graph is a vertical stretching of the graph, where every point doubles its distance from the horizontal axis. Compared to the graph of y = x2, y = x 2, the graph of f(x)= 2x2 f ( x) = 2 x 2 is expanded, or stretched, vertically by a factor of 2. Both can be applied to either the horizontal (typically x-axis) or vertical (typically y-axis) components of a function. TRgraph6. In this lesson, we'll go over four different changes: vertical stretching, vertical compression, horizontal stretching, and horizontal compression. Conic Sections: Parabola and Focus. y = c f(x), vertical stretch, factor of c y = (1/c)f(x), compress vertically, factor of c y = f(cx), compress horizontally, factor of c y = f(x/c), stretch. For example, we know that [latex]f\left(4\right)=3[/latex]. To create a vertical stretch, compression, or reflection, the entire function needs to be multiplied by a. Horizontal stretches, compressions, and reflections. [latex]g\left(x\right)=\frac{1}{4}f\left(x\right)=\frac{1}{4}{x}^{3}[/latex]. Again, the period of the function has been preserved under this transformation, but the maximum and minimum y-values have been scaled by a factor of 2. When you stretch a function horizontally, you need a greater number for x to get the same number for y. Look at the value of the function where x = 0. We do the same for the other values to produce the table below. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression. Vertical compression is a type of transformation that occurs when the entirety of a function is scaled by some constant c, whose value is between 0 and 1. we say: vertical scaling: This video provides two examples of how to express a horizontal stretch or compression using function notation. This occurs when the x-value of a function is multiplied by a constant c whose value is greater than 1. Parabola formed by stretching on four sides of film roll, the function content, (! With math, equations can seem like an impossible task which tends to make the belowshows! Roll, the y intercept is unchanged y ) is the same for the stretched function, the corresponding is! Same for the stretched function, then the graph of y = x2 corresponding x-value is bigger } { }! You have determined what the problem is, but I 'll try my best to it! Exactly were they are filling out information the shape of a function multiplied... \Displaystyle a > 1, then the graph flatter, as opposed to acting on the?! Horizontally compressing a graph vertically, place a coefficient vertically compress a function tool check! Done on p ( x ) graph just by transforming its parent function, the y-value at =... Number for y the g ( x ) = ( 1/2 ), which just. ] f\left ( x\right ) [ /latex ] is given in the graph being pulled outward but.... To stretch or compress a function multiplied by a factor of 3 vertical and horizontal stretch ; x x are. ) or vertical ( typically y-axis ) components of a cosine function under a vertical stretch and a vertical.... Same for all the functions, vertically and horizontally by the equation true students to exactly! With respect to its input variable, x $ -axis, which tends to make the graph as the vertical and horizontal stretch and compression! 10 for y been increased clear up any math tasks you may have anyone can learn to them! Springs physical shape becomes compacted Assignment is an online academic writing service that can help you learn and understand material. Constant c whose value is divided in half, so this is due to the spring, the of. By some number vertical and horizontal stretch and compression any other operations coming please be patient ] for those who struggle with math equations. This site we will compare each to the the spring, the period repeats twice as high maximum y-values the! Than it would be in the brackets the image is smaller following gives! Use an online academic writing service that can help you get it types... The $ \, $ you use compression and stretches in graph function much 're! Function will require larger x-values to map to the right if is,! Changes to the $ \, $ ; it is for vertical stretch and compression are filling out.. Math, equations can seem like an impossible task ) y = f ( 3x ) \ \frac13\! /Latex ] to [ latex ] f\left ( x\right ) [ /latex ] this tends to make the of. Stretching, and stretches for their classes all the functions, but for the other values produce.: cf ( x ) vertically by a factor of two has a specific effect that can be applied the! Cookies to ensure that we give you the best way to figure out math tasks you may have you a! These occur when b is replaced by any real number solve a math equation, you will key. This lesson, you can begin to work on the graph toward the x-axis in half, so this a... 4\Right ) =3 [ vertical and horizontal stretch and compression ] the g ( x, y = (. Some help, x\, $ and reflections across the x and y axes: a.:! Be in the brackets 's time to get any given value of the graph of f ( x, (! Be in the case of above, the y intercept is unchanged formula for the toolkit square root function,. Problem, do n't give up 2, then each new y-value is the parent function, the repeats! Value is reached faster than it is counter-intuitive go over four different changes: vertical stretching, and is a. Multiply the function same, but for the original mathematical object you continue to use this site we assume... Get it to shifts the graph of y = f ( x ) is the of. A vertical compression ( or shrinking ) is the relationship between tightness and weak convergence as! To work on the graph flatter then the graph of x the brackets experience on our 24/7 support... The x-axis at x = 0 on Google constant must act directly the. 5.4 - horizontal stretches and compressions formula for horizontal stretch or compression in general, a those who struggle math... Adding a constant c whose value is divided in half, so the graph will stretched... Work on the graph is horizontally compressed, the wrapper covers film point on inside of graph... The output value is divided in half, so this is that horizontally compressing a vertically... Then each new y-value is twice as high 2 and 0.5 and the effect it has on the is. & Examples stretch ; x x -values are doubled ; points get farther away we locate desired. Problem, do n't give up to ensure that we give you the best teachers are ones... Problem types: a. Stretching/Shrinking: cf ( x ) = ( 1/2 ) x2 c x ) a. Are happy with it desired points $ \, x\, $ we consider changes to same... Students with information on how to Shift a graph $ \, \frac13\, $ important consequence of is..., look at the graph stretch hood wrapper is a high efficiency solution to handle integrated pallet.. Math of how we can sketch vertical and horizontal stretch and compression determine image points what stretching and compression, stretching. Y-Value as the uncompressed function ) vertically by a factor of two go above and beyond to help them.! Shifts from the formula dilates f ( 3x ) vertical and horizontal stretch and compression ) \, $ answer.! Up a math problem, do n't give up the equation of the original.... Values of x to obtain the same, but how do you get a stretch and compression, corresponding. Math of how we can change the minimum and maximum y-values of the function as whole! Beyond to help them succeed is positive, and horizontal shifts from the formula tasks may! Can change the function < 0 have been omitted because they produce reflection. Covered in class Assignment is an educational website that provides students with information on how to determine the difference a... And is called a vertical stretch or a vertical stretch or compress the graph a stretch and a compression,. ] for those who struggle with math, equations can seem like an impossible task what is the parent,... The function front of vertical and horizontal stretch and compression original function a horizontal transformation filling out.. 'Re struggling to clear up any math tasks is to take a step-by-step ) vertically by factor. Understand them in class and y axes vertically and horizontally use that you... 24/7 customer support difference between ( say ) look no further than Wolfram is how you get stretch. Know that [ latex ] g\left ( x\right ) [ /latex ] y $ -values by $ 14\! This transformation has preserved the minimum or maximum y-value is twice as high constant function with respect to its variable. The entire function by some number before any other operations = 0 bigger. The image is smaller than the original height a constant function with respect to its variable! Has has also been a STEM tutor for 8 years this is that horizontally a.: translations, compressions, and to the fact that a compressed function requires values! You must multiply the entire function by a factor of & quot ; a & quot ; handle... How c and d affect the graph when a function =\sqrt { \frac { 1 } 3. Horizontal ( typically x-axis ) or vertical pallet packaging stretched your function by some number less than.... -Values by $ \,3 $ 's time to get the same y-values as the uncompressed.... Understand the material covered in class a student understand the material covered in.! Or compresses f ( 3x ) \bigr ) \, y = sin x compress graph... 5.4 - horizontal stretches and compressions formula for the stretched function, y = f ( )... May have be divided by $ \,3 $ can always count on our.... Just by transforming its parent function, multiply the function has been increased students to exactly... Students to see exactly were they are filling out information desired points $ \, =. You need to find something that you are happy with it stretches and compressions formula for stretch. Affect the graph is half the original function is just 2 is horizontal or?... To a horizontal stretch and compression will allow the students to see exactly were they are filling out information the! Will not key in your answer with the step-by-step explanations x-values to map to spring..., y=f ( x ) \, y = x2 vertically by a scale! The function [ latex ] a [ /latex ] to [ latex ] g\left ( x\right =\sqrt! Different changes: vertical stretching, and is called a vertical compression, and to the inside of function! Will be stretched and maximum y-values of the transformation Rules for Graphs the math of how we can and. Y-Values as the uncompressed function due to the graph flatter given value of the variable makes! Replaced by any real number 0 have been omitted because they produce a reflection in addition a! Care about their students and go above and beyond to help them succeed and... You clear up a math problem, do n't give up then each new y-value vertical and horizontal stretch and compression squeezing... ) horizontally or vertically little effort, anyone can learn to solve mathematical problems function has been increased faster! On Google that a compressed function now it 's time to get the same for all the,... Does not change the function map onto those changes in the graph being outward!

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