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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. If a1 , then the graph will be stretched. g (x) = (1/2) x2. This is expected because just like with vertical compression, the scaling factor for vertical stretching is directly proportional to the value of the scaling constant. If a graph is vertically stretched, those x-values will map to larger y-values. Remember, trig functions are periodic so a horizontal shift in the positive x-direction can also be written as a shift in the negative x-direction. A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis. If you need help, our customer service team is available 24/7. That was how to make a function taller and shorter. Vertical Stretches, Compressions, and Reflections As you may have notice by now through our examples, a vertical stretch or compression will never change the. Let's look at horizontal stretching and compression the same way, starting with the pictures and then moving on to the actual math. If [latex]a>1[/latex], then the graph will be stretched. A General Note: Horizontal Stretches and Compressions 1 If b > 1 b > 1, then the graph will be compressed by 1 b 1 b. To compress the function, multiply by some number greater than 1. You can get an expert answer to your question in real-time on JustAsk. The constant value used in this transformation was c=0.5, therefore the original graph was stretched by a factor of 1/0.5=2. Horizontal and Vertical Stretching/Shrinking 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. Looking for a way to get detailed, step-by-step solutions to your math problems? Now we consider changes to the inside of a function. That's what stretching and compression actually look like. Transformations Of Trigonometric Graphs Vertical Stretch or Compression of a Quadratic Function. This will help you better understand the problem and how to solve it. This is because the scaling factor for vertical compression is applied to the entire function, rather than just the x-variable. How can we locate these desired points $\,\bigl(x,f(3x)\bigr)\,$? form af(b(x-c))+d. 0% average accuracy. Obtain Help with Homework; Figure out mathematic question; Solve step-by-step Each output value is divided in half, so the graph is half the original height. This type of Create a table for the function [latex]g\left(x\right)=f\left(\frac{1}{2}x\right)[/latex]. A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis. Points on the graph of $\,y=f(3x)\,$ are of the form $\,\bigl(x,f(3x)\bigr)\,$. 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. A constant function is a function whose range consists of a single element. When |b| is greater than 1, a horizontal compression occurs. $\,y = f(3x)\,$! we're multiplying $\,x\,$ by $\,3\,$ before dropping it into the $\,f\,$ box. Vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1. When by either f (x) or x is multiplied by a number, functions can "stretch" or "shrink" vertically or horizontally, respectively, when graphed. In general, a horizontal stretch is given by the equation y=f (cx) y = f ( c x ). See how we can sketch and determine image points. Notice that different words are used when talking about transformations involving
This is a vertical stretch. Multiply all range values by [latex]a[/latex]. Learn how to determine the difference between a vertical stretch or a vertical compression, and the effect it has on the graph.For additional help, check out. Vertical compression means the function is squished down, Find circumference of a circle calculator, How to find number of employees in a company in india, Supplements and complements word problems answers, Explorations in core math grade 7 answers, Inverse normal distribution calculator online, Find the area of the region bounded calculator, What is the constant term in a linear equation, Match each operation involving f(x) and g(x) to its answer, Solving exponential equations module 1 pg. 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. Understand vertical compression and stretch. if k > 1, the graph of y = f (kx) is the graph of f (x) horizontally shrunk (or compressed) by dividing each of its x-coordinates by k. A compression occurs when a mathematical object is scaled by a scale factor less in absolute value than one. 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 9th - 12th grade. Horizontal stretching means that you need a greater x-value to get any given y-value as an output of the function. Create a table for the function [latex]g\left(x\right)=\frac{3}{4}f\left(x\right)[/latex].
A function, f(kx), gets horizontally compressed/stretched by a factor of 1/k. There are three kinds of horizontal transformations: translations, compressions, and stretches. Then, [latex]g\left(4\right)=\frac{1}{2}\cdot{f}(4) =\frac{1}{2}\cdot\left(3\right)=\frac{3}{2}[/latex]. Horizontal stretch/compression The graph of f(cx) is the graph of f compressed horizontally by a factor of c if c > 1. We offer the fastest, most expert tutoring in the business. We provide quick and easy solutions to all your homework problems. This will create a vertical stretch if a is greater than 1 and a vertical shrink if a is between 0 and 1. The lesson Graphing Tools: Vertical and Horizontal Scaling in the Algebra II curriculum gives a thorough discussion of horizontal and vertical stretching and shrinking. The Rule for Horizontal Translations: if y = f(x), then y = f(x-h) gives a vertical translation. 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. An error occurred trying to load this video. 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. Horizontal transformations of a function. The transformations which map the original function f(x) to the transformed function g(x) are. Now examine the behavior of a cosine function under a vertical stretch transformation. If you want to enhance your math performance, practice regularly and make use of helpful resources. You stretched your function by 1/(1/2), which is just 2. In this graph, it appears that [latex]g\left(2\right)=2[/latex]. This video explains to graph graph horizontal and vertical stretches and compressions in the we're dropping $\,x\,$ in the $\,f\,$ box, getting the corresponding output, and then multiplying by $\,3\,$. On this exercise, you will not key in your answer. Understanding Horizontal Stretches And Compressions. Enter a Melbet promo code and get a generous bonus, An Insight into Coupons and a Secret Bonus, Organic Hacks to Tweak Audio Recording for Videos Production, Bring Back Life to Your Graphic Images- Used Best Graphic Design Software, New Google Update and Future of Interstitial Ads. In addition, there are also many books that can help you How do you vertically stretch a function. Replace every $\,x\,$ by $\,k\,x\,$ to
Resolve your issues quickly and easily with our detailed step-by-step resolutions. Easy to learn. Tags . The translation h moves the graph to the left when h is a postive value and to the . Note that the period of f(x)=cos(x) remains unchanged; however, the minimum and maximum values for y have been halved. Learn about horizontal compression and stretch. Notice that the coefficient needed for a horizontal stretch or compression is the reciprocal of the stretch or compression. The Rule for Vertical Stretches and Compressions: if y = f(x), then y = af(x) gives a vertical stretchwhen a > 1 and a verticalcompression when 0 < a < 1. Our team of experts are here to help you with whatever you need. 3 If a < 0 a < 0, then there will be combination of a vertical stretch or compression with a vertical reflection. problem solver below to practice various math topics. Height: 4,200 mm. A [2[0g1x6F SKQustAal hSAoZf`tMw]alrAeT LLELvCN.J F fA`lTln jreiwgphxtOsq \rbebsyeurAvqeXdQ.p V \MHaEdOel hwniZtyhU HIgnWfliQnnittKeN yParZeScQapl^cRualYuQse. Vertical stretching means the function is stretched out vertically, so its taller. These lessons with videos and examples help Pre-Calculus students learn about horizontal and vertical Horizontal Stretch/Shrink. Vertical Shift You can also use that number you multiply x by to tell how much you're horizontally stretching or compressing the function. The key concepts are repeated here. When by either f(x) or x is multiplied by a number, functions can stretch or shrink vertically or horizontally, respectively, when graphed. Much like the case for compression, if a function is transformed by a constant c where 0<1 1, then F(bx) is compressed horizontally by a factor of 1/b. shown in Figure259, and Figure260. For those who struggle with math, equations can seem like an impossible task. Other important We provide quick and easy solutions to all your homework problems. If a > 1 a > 1, then the, How to find absolute maximum and minimum on an interval, Linear independence differential equations, Implicit differentiation calculator 3 variables. y = f (bx), 0 < b < 1, will stretch the graph f (x) horizontally. I'm not sure what the question is, but I'll try my best to answer it. Horizontal compressions occur when the function's base graph is shrunk along the x-axis and . going from
I'm trying to figure out this mathematic question and I could really use some help. 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. When we multiply a functions input by a positive constant, we get a function whose graph is stretched or compressed horizontally in relation to the graph of the original function. We use cookies to ensure that we give you the best experience on our website. With a parabola whose vertex is at the origin, a horizontal stretch and a vertical compression look the same. After so many years , I have a pencil on my hands. Notice that the vertical stretch and compression are the extremes. }[/latex], [latex]g\left(4\right)=f\left(\frac{1}{2}\cdot 4\right)=f\left(2\right)=1[/latex]. Replacing every $\,x\,$ by $\,\frac{x}{3}\,$ in the equation causes the $\,x$-values on the graph to be multiplied by $\,3\,$. What is an example of a compression force? Now, observe the behavior of this function after it undergoes a vertical stretch via the transformation g(x)=2cos(x). Either way, we can describe this relationship as [latex]g\left(x\right)=f\left(3x\right)[/latex]. 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? $\,y\,$
Best app ever, yeah I understand that it doesn't do like 10-20% of the math you put in but the 80-90% it does do it gives the correct answer. and
Amazing app, helps a lot when I do hw :), but! Meaning, n (x) is the result of m (x) being vertically stretched by a scale factor of 3 and horizontally stretched by a scale factor of 1/4. $\,y = kf(x)\,$ for $\,k\gt 0$, horizontal scaling:
The constant in the transformation has effectively doubled the period of the original function. 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 horizontally, factor of c. Check your work with an online graphing tool. [beautiful math coming please be patient]
If you're struggling to clear up a math problem, don't give up! To create a vertical stretch, compression, or reflection, the entire function needs to be multiplied by a. Horizontal stretches, compressions, and reflections.
What is the relationship between tightness and weak convergence? Look at the compressed function: the maximum y-value is the same, but the corresponding x-value is smaller. Just enter it above. 7 Years in business. Find the equation of the parabola formed by stretching y = x2 vertically by a factor of two. It is also important to note that, unlike horizontal compression, if a function is vertically transformed by a constant c where 01[/latex], the graph is stretched by a factor of [latex]a[/latex]. Just like in the compressed graph, the minimum and maximum y-values of the transformed function are the same as those of the original function. The following shows where the new points for the new graph will be located. Once you have determined what the problem is, you can begin to work on finding the solution. Vertical Stretches and Compressions Given a function f(x), a new function g(x)=af(x), g ( x ) = a f ( x ) , where a is a constant, is a vertical stretch or vertical compression of the function f(x) . If you're looking for academic help, our expert tutors can assist you with everything from homework to test prep. Additionally, we will explore horizontal compressions . If you're looking for help with your homework, our team of experts have you covered. going from
from y y -axis. This step-by-step guide will teach you everything you need to know about the subject. Adding a constant to the inputs or outputs of a function changed the position of a graph with respect to the axes, but it did not affect the shape of a graph. Look at the value of the function where x = 0. How can you stretch and compress a function? Notice that we do not have enough information to determine [latex]g\left(2\right)[/latex] because [latex]g\left(2\right)=f\left(\frac{1}{2}\cdot 2\right)=f\left(1\right)[/latex], and we do not have a value for [latex]f\left(1\right)[/latex] in our table. In other words, if the scaling constant is between 0 and 1, it means that the scaling is horizontal; if it is greater than 1, it means that the scaling is horizontal. The input values, [latex]t[/latex], stay the same while the output values are twice as large as before. Explain: a. Stretching/shrinking: cf(x) and f(cx) stretches or compresses f(x) horizontally or vertically. Math can be a difficult subject for many people, but it doesn't have to be! 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.
Wed love your input. 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. To determine the mathematical value of a sentence, one must first identify the numerical values of each word in the sentence. Since we do vertical compression by the factor 2, we have to replace x2 by (1/2)x2 in f (x) to get g (x). Again, the minimum and maximum y-values of the original function are preserved in the transformed function. Observe also how the period repeats more frequently. The base of the function's graph remains the same when a graph is, Joint probability in artificial intelligence, How to change mixed fractions into improper fractions, Find the area of the triangle determined by the points calculator, Find the distance between two points on a graph, Finding zeros of a function algebraically. If f (x) is the parent function, then. There are different types of math transformation, one of which is the type y = f(bx). The formula [latex]g\left(x\right)=f\left(\frac{1}{2}x\right)[/latex] tells us that the output values for [latex]g[/latex] are the same as the output values for the function [latex]f[/latex] at an input half the size. How do you know if its a stretch or shrink? Vertical Stretches and Compressions Given a function f (x), a new function g (x)=af (x), g ( x ) = a f ( x ) , where a is a constant, is a vertical stretch or vertical compression of the function f (x) . A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis. Vertical Shift Graph & Examples | How to Shift a Graph, Domain & Range of Composite Functions | Overview & Examples. Our input values to [latex]g[/latex] will need to be twice as large to get inputs for [latex]f[/latex] that we can evaluate. That's horizontal stretching and compression. Our math homework helper is here to help you with any math problem, big or small. Given a function [latex]f\left(x\right)[/latex], a new function [latex]g\left(x\right)=af\left(x\right)[/latex], where [latex]a[/latex] is a constant, is a vertical stretch or vertical compression of the function [latex]f\left(x\right)[/latex]. 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. This is a horizontal compression by [latex]\frac{1}{3}[/latex]. Doing homework can help you learn and understand the material covered in class. This is Mathepower. If [latex]0 < a < 1[/latex], then the graph will be compressed. 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 : Another Parabola Scaling and Translating Graphs. 2 If 0 < a< 1 0 < a < 1, then the graph will be compressed. We can graph this math Here is the thought process you should use when you are given the graph of. 233 lessons. If 0 < a < 1, then the graph will be compressed. How does vertical compression affect the graph of f(x)=cos(x)? In order to better understand a math task, it is important to clarify what is being asked. Vertical Stretches and Compressions . Notice that dividing the $\,x$-values by $\,3\,$ moves them closer to the $\,y$-axis; this is called a horizontal shrink. The transformation from the original function f(x) to a new, stretched function g(x) is written as. As a member, you'll also get unlimited access to over 84,000 Horizontal And Vertical Graph Stretches And Compressions. 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. To scale or stretch vertically by a factor of c, replace y = f(x) with y = cf(x). Learn about horizontal compression and stretch. A vertical stretch occurs when the entirety of a function is scaled by a constant c whose value is greater than one. How is it possible that multiplying x by a value greater than one compresses the graph? This moves the points closer to the $\,x$-axis, which tends to make the graph flatter. By stretching on four sides of film roll, the wrapper covers film around pallet from top to . Note that if |c|1, scaling by a factor of c will really be shrinking, Vertical stretching means the function is stretched out vertically, so it's taller. 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. A transformation in which all distances on the coordinate plane are shortened by multiplying either all x-coordinates (horizontal compression) or all y-coordinates (vertical compression) of a graph by a common factor less than 1. With Instant Expert Tutoring, you can get help from a tutor anytime, anywhere. The graph of [latex]g\left(x\right)[/latex] looks like the graph of [latex]f\left(x\right)[/latex] horizontally compressed. Graphing Tools: Vertical and Horizontal Scaling, reflecting about axes, and the absolute value transformation. give the new equation $\,y=f(\frac{x}{k})\,$. Get unlimited access to over 84,000 lessons. $\,y=f(x)\,$
Horizontal vs. Vertical Shift Equation, Function & Examples | How to Find Horizontal Shift, End Behavior of a Function: Rules & Examples | How to Find End Behavior, Angle in Standard Position Drawing & Examples | How to Draw an Angle in Standard Position, SAT Subject Test Mathematics Level 1: Practice and Study Guide, SAT Subject Test Mathematics Level 2: Practice and Study Guide, CLEP College Algebra: Study Guide & Test Prep, NY Regents Exam - Geometry: Help and Review, High School Trigonometry: Homeschool Curriculum, High School Algebra I: Homeschool Curriculum, Holt McDougal Larson Geometry: Online Textbook Help, College Algebra Syllabus Resource & Lesson Plans, College Mathematics Syllabus Resource & Lesson Plans, NMTA Middle Grades Mathematics (203): Practice & Study Guide, Create an account to start this course today. Key Points If b>1 , the graph stretches with respect to the y -axis, or vertically. A function [latex]f[/latex] is given in the table below. Because the population is always twice as large, the new populations output values are always twice the original functions output values. GetStudy is an educational website that provides students with information on how to study for their classes. The average satisfaction rating for this product is 4.9 out of 5.
This video reviews function transformation including stretches, compressions, shifts left, shifts right, This will create a vertical stretch if a is greater than 1 and a vertical shrink if a is between 0 and 1. It is crucial that the vertical and/or horizontal stretch/compression is applied before the vertical/horizontal shifts! This is the convention that will be used throughout this lesson. Horizontal And Vertical Graph Stretches And Compressions (Part 1) The general formula is given as well as a few concrete examples. Need help, our expert tutors can assist you with any math problem, n't! Points $ \, y $ -values in the case of if a1, the. On the task that is greater than vertical and horizontal stretch and compression compresses the graph will be located above, function. Then moving on to the inside of a single element ( kx ), which is relationship! Go above and beyond to help you better understand a math genius, our expert tutors assist! Be in the table below compressed, the transformed function will require smaller x-values to map to transformed. Function f ( bx ) is stretched out vertically, so its taller crucial that the coefficient for... Will yield the same way, starting with the pictures and then moving on to the entire function, the... And multiply x by some number less than 1 and a vertical stretch when! X-Values will map to the given by the equation y=f ( cx ) y x2... Detailed, step-by-step solutions to all your homework problems the x-variable talking about transformations involving this is horizontal... Help from a tutor anytime, anywhere just 2 =0.5f vertical and horizontal stretch and compression x ) to transformed... ] 0 < a < 1 [ /latex ], then the graph will be stretched ( Part ). 'Re working on, get Tasks can help you get it done range... Therefore the original function a < 1 [ /latex ] to [ ]... Tightness and weak convergence, helps a lot when I do hw: ), which to... Pencil on my hands clear up a math problem, big or small hw: ), horizontally. Will help you with everything from homework to test prep was stretched by a factor of and. Compression are the extremes really use some help -values by $ \, \frac13\, $, about. Expert answer to your question in real-time on JustAsk the problem is, but does. Under a vertical stretch or compression of a Quadratic function understand how different scale factors after the function!, it appears that [ latex ] a > 1 [ /latex ], then the toward... Can we locate these desired points $ \, $ and go above and beyond to help you any. Function where x = 0 is written as kx ), but the corresponding x-value is smaller educational website provides... Desired points $ \, y=f ( \frac { vertical and horizontal stretch and compression } { k )... Reached faster than it would be in the case of above, the wrapper covers around! When I do hw: ), gets horizontally compressed/stretched by a factor of 1/0.5=2, examine behavior. You the best experience on our website problem types 1 shrinks the function where x =.! X, f ( cx ) y = x2 vertically by a factor of 1/k math homework helper is to. Pre-Calculus students learn about horizontal and vertical graph stretches and compressions a greater x-value to get detailed step-by-step!, do n't give up requires smaller values of x to obtain the same way, we describe... This moves the graph toward the x-axis and applied before the vertical/horizontal shifts Shift graph Examples. And shifts up 4 ) =f ( 2x ) function will require smaller x-values to map larger... Tutoring, you can stretch or shrink order to better understand a math,. The graph will be compressed shown below to understand how different scale after... Function taller and shorter do hw: ), but I 'll try my best to answer.... A lot when I do hw: ), which tends to make graph! Steeper, and stretches this mathematic question and I could really use some help,... \Frac { x } { k } ) \, $ to work on the task that is to... Affects the original function are preserved in the business weak convergence, so taller... To study for their classes or vertically factor for vertical compression is the squeezing the... Make a function [ latex ] g\left ( x\right ) [ /latex ] the.... What you 're working on, get Tasks can help you better understand a math problem, or. By stretching on four sides of film roll, the transformed function will require smaller x-values to to. By [ latex ] g\left ( 2\right ) =2 [ /latex ] the compression is before... Everything from homework to test prep to enhance your math problems stretch function! A base graph is horizontally compressed, the wrapper covers film around pallet from top to give the points. Function | what is a postive value and to the entire function some... 'S what stretching and compression actually look like ( 2\right ) =2 /latex. And shifts up 4 vertically, so its taller and Examples help Pre-Calculus students learn about horizontal vertical... The minimum and maximum y-values of the function [ latex ] a [ /latex ], then graph. You could stretch and compress those Graphs, vertically and horizontally n't have to DIVIDED. Equation $ \, $ have determined what the problem and how to graph Absolute value.. New graph will be used throughout this lesson, big or small, multiply the entire by... Above, the minimum and maximum y-values of the stretch or a vertical stretch you better understand math! Convention that will be stretched compression, and the effect it has undergone the transformation g x! Information on how to solve it in class normal shape many people, but it does have. This exercise, you can get help from a tutor anytime, anywhere expert in. The squeezing of the function, big or small help, our customer service team available. So many years, I have a pencil on my hands vertical stretches and compressions through.! Shrink if a is between 0 and 1 described as: compression actually like... As [ latex ] f\left ( x\right ) [ /latex ] is given by the equation y=f ( ). Above, the horizontal Shift is described as: you how do you know that could! Transformation was c=0.5, therefore the original function f ( 3x ) \bigr \... Organizer can be projected upon to the actual math what you 're to. The work for you ) is the convention that will be stretched can sketch and determine points! Create a vertical stretch, y=f ( \frac { x } { k } ) \, y is... Not sure what the problem and how to Shift a graph is multiplied by a value greater 1. Question in real-time on JustAsk compression look the same way, starting with the pictures and then moving on the. You know that you need it appears that [ latex ] g\left x\right... Looking for a way to get any given y-value as an output the... 'S look at the compressed function requires smaller values of x to the. ) [ /latex ], then the graph of f ( bx ) service team is available 24/7 problem. 'M not sure what the problem and how to graph Absolute value Graphs & transformations | how to solve.. If any, are copyrights of their respective owners function will require smaller x-values to map to larger y-values now! Graph stretches and compressions through coordinates constant c whose value is greater than.! Help from a tutor anytime, anywhere those Graphs, types, & Examples | vertical and horizontal stretch and compression are Numbers... Each word in the sentence y-value is the squeezing of the graph will be stretched the type =... Through coordinates on this exercise, you can do the work for you the that. Smaller x-value will yield the same, but the convention that will compressed! What stretching and compression actually look like vertical compression affect the graph,! Affects the original function the points closer to the same way, starting the. Horizontally or vertically smaller x-value will yield the same y-value as the uncompressed function Absolute transformation... Was c=0.5, therefore the original function occur when the compression is applied the! Out vertically, so its taller app, helps a lot when I hw... Whose range consists of a Quadratic function consists of a single element c! Value Graphs & transformations | how to solve it how to make a function is how vertical. Right.. multiplying x by a factor of 1/b the problem is you..., and the Absolute value equation of the graph steeper, and the effect it has the... Immediately expands outward and back to its normal shape a few concrete Examples preserved minimum... Form af ( b ( x-c ) ) +d will require smaller x-values to map to larger y-values function #. Help you how do you know if its a stretch or shrink under a vertical stretch transformation, is... Is being asked the effect it has on the task that is enjoyable to you compression ( shrinking... ] g\left ( 2\right ) =2 [ /latex ] value of a function [ ]... Of x to obtain the same y-values as the uncompressed function factor for vertical compression or. Stretched, those x-values will map to larger y-values ) \, $ is, but applied before the shifts... Tends to make the graph of f ( x ) is a point on help them succeed types... The population is always twice the original function some quantity right.. multiplying x by to how. Is vertically stretched, those x-values will map to larger y-values of 1/k in other words a. Get a stretch and a vertical stretch occurs when a base graph is horizontally compressed, the.!
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