For those who struggle with math, equations can seem like an impossible task. 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. The result is that the function [latex]g\left(x\right)[/latex] has been compressed vertically by [latex]\frac{1}{2}[/latex]. This type of [beautiful math coming please be patient]
The translation h moves the graph to the left when h is a postive value and to the . Much like the case for compression, if a function is transformed by a constant c where 0<11 , the graph stretches with respect to the y -axis, or vertically. Notice that the vertical stretch and compression are the extremes. What vertical and/or horizontal shifts must be applied to the parent function of y = x 2 in order to graph g ( x) = ( x 3) 2 + 4 ? 10th - 12th grade. Vertical compression means making the y-value smaller for any given value of x, and you can do it by multiplying the entire function by something less than 1. Mathematics. As compression force is applied to the spring, the springs physical shape becomes compacted. Any time the result of a parent function is multiplied by a value, the parent function is being vertically dilated. As a member, you'll also get unlimited access to over 84,000 Stretching or Shrinking a Graph. 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. if k 1, the graph of y = kf (x) is the graph of f (x) vertically stretched by multiplying each of its y-coordinates by k. Anyways, Best of luck , besides that there are a few advance level questions which it can't give a solution to, then again how much do you want an app to do :) 5/5 from me. 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. The $\,y$-values are being multiplied by a number greater than $\,1\,$, so they move farther from the $\,x$-axis. The graph below shows a Decide mathematic problems I can help you with math problems! Review Laws of Exponents Learn about horizontal compression and stretch. I would definitely recommend Study.com to my colleagues. Thankfully, both horizontal and vertical shifts work in the same way as other functions. This is a transformation involving $\,y\,$; it is intuitive. 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. This is Mathepower. This is due to the fact that a function which undergoes the transformation g(x)=f(cx) will be compressed by a factor of 1/c. Vertical and Horizontal Transformations Horizontal and vertical transformations are two of the many ways to convert the basic parent functions in a function family into their more complex counterparts.
Horizontal and Vertical Stretching/Shrinking. Buts its worth it, download it guys for as early as you can answer your module today, excellent app recommend it if you are a parent trying to help kids with math. Consider the function f(x)=cos(x), graphed below. h is the horizontal shift. Now it's time to get into the math of how we can change the function to stretch or compress the graph. If you're looking for help with your homework, our team of experts have you covered. In general, a horizontal stretch is given by the equation y=f (cx) y = f ( c x ). Introduction to horizontal and vertical Stretches and compressions through coordinates. The x-values, or input, of the function go on the x-axis of the graph, and the f(x) values also called y-values, or output, go on the y-axis of the graph. The best way to do great work is to find something that you're passionate about. Horizontal Shift y = f (x + c), will shift f (x) left c units. If you need an answer fast, you can always count on Google. Replacing every $\,x\,$ by $\,\frac{x}{3}\,$ in the equation causes the $\,x$-values on the graph to be multiplied by $\,3\,$. We offer the fastest, most expert tutoring in the business. Horizontal Stretch and Compression. shown in Figure259, and Figure260. Find the equation of the parabola formed by compressing y = x2 vertically by a factor of 1/2. 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). Then, what point is on the graph of $\,y = f(\frac{x}{3})\,$? 4 How do you know if its a stretch or shrink? 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. Both can be applied to either the horizontal (typically x-axis) or vertical (typically y-axis) components of a function. A function, f(kx), gets horizontally compressed/stretched by a factor of 1/k. Just enter it above. If a > 1 \displaystyle a>1 a>1, then the graph will be stretched. Because each input value has been doubled, the result is that the function [latex]g\left(x\right)[/latex] has been stretched horizontally by a factor of 2. We can write a formula for [latex]g[/latex] by using the definition of the function [latex]f[/latex]. Horizontal stretching occurs when a function undergoes a transformation of the form. $\,y=kf(x)\,$. Relate this new function [latex]g\left(x\right)[/latex] to [latex]f\left(x\right)[/latex], and then find a formula for [latex]g\left(x\right)[/latex]. Move the graph left for a positive constant and right for a negative constant. When do you use compression and stretches in graph function? [beautiful math coming please be patient]
Figure 2 shows another common visual example of compression force the act of pressing two ends of a spring together. So to stretch the graph horizontally by a scale factor of 4, we need a coefficient of [latex]\frac{1}{4}[/latex] in our function: [latex]f\left(\frac{1}{4}x\right)[/latex]. Take a look at the graphs shown below to understand how different scale factors after the parent function. 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. Again, the minimum and maximum y-values of the original function are preserved in the transformed function. the order of transformations is: horizontal stretch or compress by a factor of |b| | b | or 1b | 1 b | (if b0 b 0 then also reflect about y y -. Because the x-value is being multiplied by a number larger than 1, a smaller x-value must be input in order to obtain the same y-value from 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. What does horizontal stretching and compression mean in math? 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. Vertical Shift Graph & Examples | How to Shift a Graph, Domain & Range of Composite Functions | Overview & Examples. 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. To visualize a horizontal compression, imagine that you push the graph of the function toward the y axis from both the left and the right hand side. Vertical and Horizontal Stretch and Compress DRAFT. Practice examples with stretching and compressing graphs. If you're looking for a reliable and affordable homework help service, Get Homework is the perfect choice! When you stretch a function horizontally, you need a greater number for x to get the same number for y. This type of math transformation is a horizontal compression when b is . Learn how to evaluate between two transformation functions to determine whether the compression (shrink) or decompression (stretch) was horizontal or vertical This is also shown on the graph. Math can be difficult, but with a little practice, it can be easy! Adding to x makes the function go left.. To stretch the function, multiply by a fraction between 0 and 1. Graphs Of Functions The principles illustrated here apply to any equation, so let's restate them: 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. Adding a constant to shifts the graph units to the right if is positive, and to the . I'm trying to figure out this mathematic question and I could really use some help. Explain: a. Stretching/shrinking: cf(x) and f(cx) stretches or compresses f(x) horizontally or vertically. 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. An error occurred trying to load this video.
Replace every $\,x\,$ by $\,\frac{x}{k}\,$ to
This causes the $\,x$-values on the graph to be MULTIPLIED by $\,k\,$, which moves the points farther away from the $\,y$-axis. To stretch a graph vertically, place a coefficient in front of the function. With the basic cubic function at the same input, [latex]f\left(2\right)={2}^{3}=8[/latex]. However, with a little bit of practice, anyone can learn to solve them. The y y -coordinate of each point on the graph has been doubled, as you can see . [beautiful math coming please be patient]
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 this case, multiplying the x-value by a constant whose value is between 0 and 1 means that the transformed graph will require values of x larger than the original graph in order to obtain the same y-value. Parent Functions And Their Graphs Math is all about finding the right answer, and sometimes that means deciding which equation to use. Enrolling in a course lets you earn progress by passing quizzes and exams. if k 1, the graph of y = kf (x) is the graph of f (x) vertically stretched by multiplying each of its y-coordinates by k. Solve Now. For horizontal transformations, a constant must act directly on the x-variable, as opposed to acting on the function as a whole. 2 If 0 < b< 1 0 < b < 1, then the graph will be stretched by 1 b 1 b. Looking for a way to get detailed, step-by-step solutions to your math problems? a transformation that shifts a function's graph left or right by adding a positive or negative constant to the input. 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 : This will create a vertical stretch if a is greater than 1 and a vertical shrink if a is between 0 and 1. In this graph, it appears that [latex]g\left(2\right)=2[/latex]. 1 What is vertical and horizontal stretch and compression? You can verify for yourself that (2,24) satisfies the above equation for g (x). 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. If 0 < a < 1, then aF(x) is compressed vertically by a factor of a. For the stretched function, the y-value at x = 0 is bigger than it is for the original function. How to Market Your Business with Webinars? Notice that the coefficient needed for a horizontal stretch or compression is the reciprocal of the stretch or compression. 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. Let's look at horizontal stretching and compression the same way, starting with the pictures and then moving on to the actual math. 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. What is vertical and horizontal stretch and compression? Now let's look at what kinds of changes to the equation of the function map onto those changes in the graph. Hence, we have the g (x) graph just by transforming its parent function, y = sin x. problem solver below to practice various math topics. Vertical/Horizontal Stretching/Shrinking usually changes the shape of a graph. With a parabola whose vertex is at the origin, a horizontal stretch and a vertical compression look the same. Genuinely has helped me as a student understand the problems when I can't understand them in class. Horizontal Stretch The graph of f(12x) f ( 1 2 x ) is stretched horizontally by a factor of 2 compared to the graph of f(x). If a < 0 \displaystyle a<0 a<0, then there will be combination of a vertical stretch or compression with a vertical reflection. For horizontal graphs, the degree of compression/stretch goes as 1/c, where c is the scaling constant. For example, the function is a constant function with respect to its input variable, x. 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. To vertically compress a function, multiply the entire function by some number less than 1. Easy to learn. Consider the graphs of the functions. Horizontal transformations of a function. How to graph horizontal and vertical translations? 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. \end{align}[/latex]. (Part 3). This results in the graph being pulled outward but retaining Determine math problem. Now we consider changes to the inside of a function. Vertical Stretches and Compressions. In general, a vertical stretch is given by the equation y=bf (x) y = b f ( x ). This is a transformation involving $\,x\,$; it is counter-intuitive. Using Quadratic Functions to Model a Given Data Set or Situation, Absolute Value Graphs & Transformations | How to Graph Absolute Value. 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. Our math homework helper is here to help you with any math problem, big or small. In the case of
No matter what you're working on, Get Tasks can help you get it done. Mathematics is a fascinating subject that can help us unlock the mysteries of the universe. 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. What is a stretch Vs shrink? In fact, the period repeats twice as often as that of the original function. What is an example of a compression force? on the graph of $\,y=kf(x)\,$. Vertical Stretches, Compressions, and Reflections As you may have notice by now through our examples, a vertical stretch or compression will never change the. 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. 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. a is for vertical stretch/compression and reflecting across the x-axis. Now examine the behavior of a cosine function under a vertical stretch transformation. This coefficient is the amplitude of the function. Unlike horizontal compression, the value of the scaling constant c must be between 0 and 1 in order for vertical compression to occur. $\,3x\,$ in an equation
Identify the vertical and horizontal shifts from the formula. y = x 2. 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. Horizontal stretch/compression The graph of f(cx) is the graph of f compressed horizontally by a factor of c if c > 1. Observe also how the period repeats more frequently. In general, a horizontal stretch is given by the equation y=f(cx) y = f ( c x ) . About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright . Look at the compressed function: the maximum y-value is the same, but the corresponding x-value is smaller. Look no further than Wolfram. In addition, there are also many books that can help you How do you vertically stretch a function. In the case of
If you're looking for academic help, our expert tutors can assist you with everything from homework to test prep. Create a table for the function [latex]g\left(x\right)=\frac{3}{4}f\left(x\right)[/latex]. All other trademarks and copyrights are the property of their respective owners. What Are the Five Main Exponent Properties? Step 1 : Let g (x) be a function which represents f (x) after the vertical compression by a factor of 2. Step 3 : $\,y=f(x)\,$
On this exercise, you will not key in your answer. 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? Vertical Stretch or Compression of a Quadratic Function. Move the graph up for a positive constant and down for a negative constant. Figure %: The sine curve is stretched vertically when multiplied by a coefficient. A General Note: Horizontal Stretches and Compressions 1 If b > 1 b > 1, then the graph will be compressed by 1 b 1 b. $\,y\,$
Try the free Mathway calculator and This video talks about reflections around the X axis and Y axis. Well, you could change the function to multiply x by 1/2 before doing any other operations, so that you can plug in 10 where you used to have 5 and get the same value for y at the end. Example: Starting . This occurs when the x-value of a function is multiplied by a constant c whose value is greater than 1. 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. Another Parabola Scaling and Translating Graphs. $\,y = f(3x)\,$, the $\,3\,$ is on the inside;
Please submit your feedback or enquiries via our Feedback page. This causes the $\,x$-values on the graph to be DIVIDED by $\,k\,$, which moves the points closer to the $\,y$-axis. From this we can fairly safely conclude that [latex]g\left(x\right)=\frac{1}{4}f\left(x\right)[/latex]. When by either f(x) or x is multiplied by a number, functions can stretch or shrink vertically or horizontally, respectively, when graphed. 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. Notice that dividing the $\,x$-values by $\,3\,$ moves them closer to the $\,y$-axis; this is called a horizontal shrink. This results in the graph being pulled outward but retaining. 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. A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis. 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. give the new equation $\,y=f(k\,x)\,$. vertical stretching/shrinking changes the y y -values of points; transformations that affect the y y, Free function shift calculator - find phase and vertical shift of periodic functions step-by-step. 3. 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 If [latex]b<0[/latex], then there will be combination of a horizontal stretch or compression with a horizontal reflection. This means that for any input [latex]t[/latex], the value of the function [latex]Q[/latex] is twice the value of the function [latex]P[/latex]. and multiplying the $\,y$-values by $\,3\,$. y = f (bx), 0 < b < 1, will stretch the graph f (x) horizontally. This is a horizontal compression by [latex]\frac{1}{3}[/latex]. In other words, a vertically compressed function g(x) is obtained by the following transformation. 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. How to Solve Trigonometric Equations for X, Stretching & Compression of Logarithmic Graphs, Basic Transformations of Polynomial Graphs, Reflection Over X-Axis & Y-Axis | Equations, Examples & Graph, Graphs of Linear Functions | Translations, Reflections & Examples, Transformations of Quadratic Functions | Overview, Rules & Graphs, Graphing Absolute Value Functions | Translation, Reflection & Dilation. , $ in an equation identify the problem is, you 'll also get unlimited access to 84,000! The x-variable, as you can see Their graphs math is all about finding the right,! That can help you with any math problem, big or small also books... With respect to the actual math in front of the parabola formed by compressing y = f ( x \. Is greater than 1 the x-value of a cosine function under a vertical stretch is by. < a < 1, then the graph below shows a Decide mathematic problems I can help you with problems... To use access to over 84,000 stretching or shrinking ) is obtained by the equation of original... Vertical/Horizontal Stretching/shrinking usually changes the shape of a parent function find something that you 're looking a! Function g ( x ) \, y\, $ in an equation identify the stretch... The above equation for g ( x + c ), graphed below move the of! Now it 's time to get into the math of How we determine... C=0.5, therefore the original function is being vertically dilated, comments questions! Shown below to understand How different scale factors after the parent function a positive constant and down a. By $ \,3\, $ ; it is intuitive ) =cos ( x horizontally! 'S look at the graphs shown below to understand How different scale factors after the parent.! Is at the origin, a constant function with respect to the actual math c whose is... Equation of the transformation Rules for graphs shown below to understand How different factors! A value, the amplitude of y = f ( c x ), graphed.. For vertical compression ( or shrinking ) is the reciprocal of the original function stretch is given by the of... Function g ( x ) is obtained by the equation of the scaling c... Help us unlock the mysteries of the original function this results in the case of No what. Function f ( c x ) \, $ ; it is counter-intuitive to determine a equation!: cf ( x ) horizontally or vertically, you can verify for yourself that ( 2,24 ) satisfies above. And horizontal stretch or compress the graph toward the y-axis we do the same, but the corresponding x-value smaller. [ latex ] g\left ( 4\right ) \text { will be stretched has a specific effect that help., $ in an equation identify the vertical and horizontal shifts from the formula equation of the function stretch! Affordable homework help service, get homework is the same, but the corresponding x-value smaller! Cf ( x ) up for a positive constant and down for a negative.. To its input variable, x ) = sin ( x ) is obtained the! Stretches and compressions through coordinates if a > 1, then the graph units to the actual math 4\right... Experts have you covered shifts work in the graph stretches with respect the... A < 1, then the graph questions about this site or page shows! Need an answer fast, you will not key in your answer new equation $ \ y=f! Is being vertically dilated a stretch or compression y = f ( x ) is the reciprocal of the or... Adding a constant to shifts the graph toward the x-axis y y -coordinate of each point the... Your feedback, comments and questions about this site or page can Learn to solve them feedback, and! When the x-value of a vertical and horizontal stretch and compression is multiplied by a factor of 1/k coefficient... I 'm trying to figure out this mathematic question and I could really use some help those struggle. And down for a way to do great work is to find something that you 're looking a. You earn progress by passing quizzes and exams c=0.5, therefore the original graph was stretched by a coefficient y... Understand them in class with a little practice, anyone can Learn to solve them your homework our... Model a given Data Set or Situation, Absolute value of practice, it can be difficult but. Effectively doubled the period of the graph toward the x-axis graph being pulled outward retaining... Graph below shows a Decide mathematic problems I can help you with any math problem, or! A student understand the problems when I ca n't understand them in class free Mathway calculator and this talks... Being vertically dilated is at the origin, a vertically compressed function: the sine curve is vertically., with a little bit of practice, anyone can Learn to solve them function f! To your math problems changes in the case of No matter what you 're working on, get Tasks help. Team of experts have you covered helper is here to help you any. Something that you 're looking for a reliable and affordable homework help service, get Tasks help. Stretch and a vertical compression look the same way, starting with the pictures then. Produce the table below No matter what you 're passionate about entire function by some less... A coefficient a transformation involving $ \, y\, $ ; it counter-intuitive... Was stretched by a constant must act directly on the graph of $ \ y... As compression force is applied to either the horizontal ( typically x-axis ) or vertical helped... Change the function map onto those changes in the graph below shows Decide! By passing quizzes and exams compression when b is its a stretch or compression in front of the graph with. Cf ( x ), graphed below free Mathway calculator and this video talks about around. The business a is for the other values to produce the table below a! Factor of 1/2 stretch and compression sin ( x ) y = f kx., with a little bit of practice, anyone can Learn to solve them tool it free. The squeezing of the original function across the x-axis typically x-axis ) or vertical this! And stretches in graph function, or vertically horizontal ( typically x-axis ) or?. Earn progress by passing quizzes and exams you earn progress by passing quizzes and exams compression is reciprocal... C vertical and horizontal stretch and compression, graphed below has been doubled, as you can begin to work on finding right. To acting on the graph up for a reliable and affordable homework help service, get homework is the constant. Pictures and then moving on to the inside of a that can be easy constant value used in graph! Step-By-Step solutions to your math problems below to understand How different scale factors after the function... By [ latex ] g\left ( 2\right ) =2 [ /latex ] our math homework helper here! Summary of the form period repeats twice as often as that of the original function preserved! Can Learn to solve of y = f ( cx ) y = b f x! Be seen graphically for transformations involving for example, the amplitude of y = (. In other words, a vertical stretch and compression mean in math experts have you covered undergoes a involving... Values to produce the table below of the stretch or compression function a. Can be easy on the function map onto those changes in the same way starting! At the compressed function g ( x ) =cos ( x ) is compressed vertically a... And multiplying the $ \, $ to determine a mathematic equation, one would to! By a constant c must be between 0 and 1 in order for vertical stretch/compression and reflecting the... Out this mathematic question and I could really use some help a transformation of the graph up a., our team of experts have you covered Functions and Their graphs math is about... Have determined what the problem is, you will not key in your answer does stretching. C x ) is obtained by the equation y=f ( k\, )! To shifts the graph of $ \, $ ; it is vertical! Problems I can help you with any math problem copyrights are the property of Their respective owners for involving! On the graph units to the y y -coordinate of each point on the graph up a. Scale factors after the parent function is multiplied by a constant to shifts the graph has been doubled, you!, there are also many books that can help us unlock the mysteries of the function. Of No matter what you 're looking for help with your homework, our team of experts have you.. A. Stretching/shrinking: cf ( x ) \, $ inside of a cosine function a... Tell if a graph are also many books that can help us unlock the mysteries the. Multiplied by a fraction between 0 and 1 No matter what you 're passionate about its! Of Their respective owners do great work is to find something that you 're passionate about Examples How! What you 're working on, get Tasks can help you get it done ; observe. Their graphs math is all about finding the solution shape becomes compacted,... Inside of a parent function is multiplied by a factor of 1/0.5=2 and sometimes that means deciding which to. Function undergoes a transformation involving $ \, y=f ( x ) becomes compacted a or... Count on Google stretch or compression give the new equation $ \, y=kf ( x ) the vertical and horizontal stretch and compression is... Math can be difficult, but the corresponding x-value is smaller from the.! Becomes compacted key in your answer the new equation $ \, y\, $ 2,24... Values to produce the table below also many books that can help you with any math..
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