Vertical Stretch or Compression of a Quadratic Function. $\,y = kf(x)\,$ for $\,k\gt 0$, horizontal scaling:
How can we locate these desired points $\,\bigl(x,f(3x)\bigr)\,$? 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. 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 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. Consider the function f(x)=cos(x), graphed below. Other important $\,y\,$, and transformations involving $\,x\,$. horizontal stretch; x x -values are doubled; points get farther away. 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 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. When you stretch a function horizontally, you need a greater number for x to get the same number for y. Learn about horizontal compression and stretch. Do a horizontal stretch; the $\,x$-values on the graph should get multiplied by $\,2\,$. However, in this case, it can be noted that the period of the function has been increased. Replacing every $\,x\,$ by $\,\frac{x}{3}\,$ in the equation causes the $\,x$-values on the graph to be multiplied by $\,3\,$. 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. going from
49855+ Delivered assignments. It looks at how c and d affect the graph of f(x). For horizontal transformations, a constant must act directly on the x-variable, as opposed to acting on the function as a whole. $\,y = f(x)\,$
Why are horizontal stretches opposite? If you continue to use this site we will assume that you are happy with it. 3. Lastly, let's observe the translations done on p (x). To stretch the function, multiply by a fraction between 0 and 1. Whats the difference between vertical stretching and compression? The horizontal shift depends on the value of . This video reviews function transformation including stretches, compressions, shifts left, shifts right, 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. How to Market Your Business with Webinars? This process works for any function. Figure 3 . Say that we take our original function F(x) and multiply x by some number b. Thats what stretching and compression actually look like. You stretched your function by 1/(1/2), which is just 2. Vertical Shift Graph & Examples | How to Shift a Graph, Domain & Range of Composite Functions | Overview & Examples. After so many years , I have a pencil on my hands. Now you want to plug in 10 for x and get out 10 for y. Vertical Stretches and Compressions . If you're looking for help with your homework, our team of experts have you covered. If [latex]0 < a < 1[/latex], then the graph will be compressed. More Pre-Calculus Lessons. 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 are Vertical Stretches and Shrinks? Try the given examples, or type in your own 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. Acquiring the tools for success, students must hone their skillset and know How to write a vertical compression to stay competitive in today's educational environment. Notice that the coefficient needed for a horizontal stretch or compression is the reciprocal of the stretch or compression. Vertical Stretches, Compressions, and Reflections As you may have notice by now through our examples, a vertical stretch or compression will never change the. 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). Example: Starting . Both can be applied to either the horizontal (typically x-axis) or vertical (typically y-axis) components of a function. This video explains to graph graph horizontal and vertical stretches and compressions in the Create a table for the function [latex]g\left(x\right)=\frac{3}{4}f\left(x\right)[/latex]. In fact, the period repeats twice as often as that of the original function. For transformations involving
Vertical compression means the function is squished down vertically, so it's shorter. vertical stretch wrapper. Math can be difficult, but with a little practice, it can be easy! Easy to learn. There are plenty of resources and people who can help you out. 2 If 0 < a< 1 0 < a < 1, then the graph will be compressed. Here is the thought process you should use when you are given the graph of $\,y=f(x)\,$. 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. You can verify for yourself that (2,24) satisfies the above equation for g (x). to
For example, look at the graph of a stretched and compressed function. Horizontal transformations of a function. In general, a vertical stretch is given by the equation y=bf (x) y = b f ( x ). Step 1 : Let g (x) be a function which represents f (x) after the vertical compression by a factor of 2. The formula for each horizontal transformation is as follows: In each case, c represents some constant, often referred to as a scaling constant. Thus, the graph of $\,y=f(3x)\,$ is the same as the graph of $\,y=f(x)\,$. fully-automatic for the food and beverage industry for loads. we say: vertical scaling:
Now let's look at what kinds of changes to the equation of the function map onto those changes in the graph. Math can be difficult, but with a little practice, it can be easy! Figure 4. 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. Multiply the previous $\,y\,$-values by $\,k\,$, giving the new equation
Try the free Mathway calculator and If a1 , then the graph will be stretched. [beautiful math coming please be patient]
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. This type of Divide x-coordinates (x, y) becomes (x/k, y). Give examples of when horizontal compression and stretch can be used. 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. from y y -axis. we're multiplying $\,x\,$ by $\,3\,$ before dropping it into the $\,f\,$ box. It shows you the method on how to do it too, so once it shows me the answer I learn how the method works and then learn how to do the rest of the questions on my own but with This apps method! 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. 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 ? Do a vertical shrink, where $\,(a,b) \mapsto (a,\frac{b}{4})\,$. \end{align}[/latex]. If you need help, our customer service team is available 24/7. In the case of
lessons in math, English, science, history, and more. Vertical and Horizontal Stretch & Compression of a Function Vertical Stretches and Compressions. horizontal stretch; x x -values are doubled; points get farther away. When by either f (x) or x is multiplied by a number, functions can "stretch" or "shrink" vertically or horizontally, respectively, when graphed. If [latex]a>1[/latex], the graph is stretched by a factor of [latex]a[/latex]. 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. [latex]\begin{cases}\left(0,\text{ }1\right)\to \left(0,\text{ }2\right)\hfill \\ \left(3,\text{ }3\right)\to \left(3,\text{ }6\right)\hfill \\ \left(6,\text{ }2\right)\to \left(6,\text{ }4\right)\hfill \\ \left(7,\text{ }0\right)\to \left(7,\text{ }0\right)\hfill \end{cases}[/latex], Symbolically, the relationship is written as, [latex]Q\left(t\right)=2P\left(t\right)[/latex]. 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. Meanwhile, for horizontal stretch and compression, multiply the input value, x, by a scale factor of a. A shrink in which a plane figure is . In the case of above, the period of the function is . For the compressed function, the y-value is smaller. If you want to enhance your math performance, practice regularly and make use of helpful resources. Linear Horizontal/Vertical Compression&Stretch Organizer and Practice. Length: 5,400 mm. The original function looks like. This is the opposite of vertical stretching: whatever you would ordinarily get out of the function, you multiply it by 1/2 or 1/3 or 1/4 to get the new, smaller y-value. on the graph of $\,y=kf(x)\,$. dilates f (x) vertically by a factor of "a". Given a function [latex]y=f\left(x\right)[/latex], the form [latex]y=f\left(bx\right)[/latex] results in a horizontal stretch or compression. The Rule for Horizontal Translations: if y = f(x), then y = f(x-h) gives a vertical translation.
h is the horizontal shift. You can also use that number you multiply x by to tell how much you're horizontally stretching or compressing the function. 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 [latex]b<0[/latex], then there will be combination of a horizontal stretch or compression with a horizontal reflection. I feel like its a lifeline. For example, if you multiply the function by 2, then each new y-value is twice as high. If a graph is vertically stretched, those x-values will map to larger y-values. This moves the points closer to the $\,x$-axis, which tends to make the graph flatter. How do you know if a stretch is horizontal or vertical? 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. 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. ), HORIZONTAL AND VERTICAL STRETCHING/SHRINKING. Explain how to indetify a horizontal stretch or shrink and a vertical stretch or shrink. Has has also been a STEM tutor for 8 years. Consider a function f(x), which undergoes some transformation to become a new function, g(x). Horizontal compression means that you need a smaller x-value to get any given y-value. 1 What is vertical and horizontal stretch and compression? If 0 < a < 1, then the graph will be compressed. With the basic cubic function at the same input, [latex]f\left(2\right)={2}^{3}=8[/latex]. 17. 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. 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. 0% average accuracy. and
Replacing every $\,x\,$ by
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. Width: 5,000 mm. Ryan Guenthner holds a BA in physics and has studied chemistry and biology in depth as well. All other trademarks and copyrights are the property of their respective owners. I would definitely recommend Study.com to my colleagues. 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. Need help with math homework? 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. If we choose four reference points, (0, 1), (3, 3), (6, 2) and (7, 0) we will multiply all of the outputs by 2. Students are asked to represent their knowledge varying ways: writing, sketching, and through a final card sort. Notice how this transformation has preserved the minimum and maximum y-values of the original function. 2. The transformations which map the original function f(x) to the transformed function g(x) are. From this we can fairly safely conclude that [latex]g\left(x\right)=\frac{1}{4}f\left(x\right)[/latex]. Just keep at it and you'll eventually get it. I'm great at math and I love helping people, so this is the perfect gig for me! Given a function f (x) f ( x), a new function g(x) = af (x) g ( x) = a f ( x), where a a is a constant, is a vertical stretch or vertical compression of the function f (x) f ( x). If you want to enhance your educational performance, focus on your study habits and make sure you're getting enough sleep. Find the equation of the parabola formed by stretching y = x2 vertically by a factor of two. No matter what math problem you're trying to solve, there are some basic steps you can follow to figure it out. Either way, we can describe this relationship as [latex]g\left(x\right)=f\left(3x\right)[/latex]. This is Mathepower. Vertical Shift The value of describes the vertical stretch or compression of the graph. If the graph is horizontally stretched, it will require larger x-values to map to the same y-values as the original function. Copyright 2005, 2022 - OnlineMathLearning.com. 4 How do you know if its a stretch or shrink? To determine a mathematic equation, one would need to first identify the problem or question that they are trying to solve. Learn about horizontal compression and stretch. and multiplying the $\,y$-values by $\,3\,$. How to Do Horizontal Stretch in a Function Let f(x) be a function.
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. Stretch hood wrapper is a high efficiency solution to handle integrated pallet packaging. If [latex]0 1 a > 1, then the, How to find absolute maximum and minimum on an interval, Linear independence differential equations, Implicit differentiation calculator 3 variables. give the new equation $\,y=f(k\,x)\,$. With a little effort, anyone can learn to solve mathematical problems. Any time the result of a parent function is multiplied by a value, the parent function is being vertically dilated. Mathematics is the study of numbers, shapes, and patterns. Understanding Horizontal Stretches And Compressions. A function that is vertically stretched has bigger y-values for any given value of x, and a function that is vertically compressed has smaller y-values for any given value of x. Let g(x) be a function which represents f(x) after an horizontal stretch by a factor of k. where, k > 1. Vertical Stretches and Compressions. How to graph horizontal and vertical translations? This coefficient is the amplitude of the function. What is the relationship between tightness and weak convergence? $\,y=f(x)\,$
If f (x) is the parent function, then. Step 10. 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. Move the graph left for a positive constant and right for a negative constant. To unlock this lesson you must be a Study.com Member. 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 : Increased by how much though? Even though I am able to identify shifts in the exercise below, 1) I still don't understand the difference between reflections over x and y axes in terms of how they are written. 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. [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). Write a formula to represent the function. Get math help online by speaking to a tutor in a live chat. 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. 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. Transformations Of Trigonometric Graphs Which function represents a horizontal compression? [beautiful math coming please be patient]
We will compare each to the graph of y = x2. You can get an expert answer to your question in real-time on JustAsk. It is divided into 4 sections, horizontal stretch, horizontal compression, Vertical stretch, and vertical compression. $\,y = f(k\,x)\,$ for $\,k\gt 0$. g (x) = (1/2) x2. Let g(x) be a function which represents f(x) after an horizontal stretch by a factor of k. Solving math equations can be challenging, but it's also a great way to improve your problem-solving skills. That was how to make a function taller and shorter. In order to better understand a math task, it is important to clarify what is being asked. Write the formula for the function that we get when we vertically stretch (or scale) the identity toolkit function by a factor of 3, and then shift it down by 2 units. math transformation is a horizontal compression when b is greater than one. a is for vertical stretch/compression and reflecting across the x-axis. There are three kinds of horizontal transformations: translations, compressions, and stretches. . Horizontal And Vertical Graph Stretches And Compressions. Looking for a way to get detailed, step-by-step solutions to your math problems? vertical stretch wrapper. There are different types of math transformation, one of which is the type y = f(bx). A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis. copyright 2003-2023 Study.com. A point $\,(a,b)\,$ on the graph of $\,y=f(x)\,$ moves to a point $\,(k\,a,b)\,$ on the graph of, DIFFERENT WORDS USED TO TALK ABOUT TRANSFORMATIONS INVOLVING $\,y\,$ and $\,x\,$, REPLACE the previous $\,x$-values by $\ldots$, Make sure you see the difference between (say), we're dropping $\,x\,$ in the $\,f\,$ box, getting the corresponding output, and. 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. vertically stretched by a factor of 8 and reflected in the x-axis (a=-8) horizontally stretched by a factor of 2 (k=1/2) translated 2 units left (d=-2) translated 3 units down (c=-3) Step 3 B egin. GetStudy is an educational website that provides students with information on how to study for their classes. To stretch a graph vertically, place a coefficient in front of the function. 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. Recall the original function. [beautiful math coming please be patient]
Two kinds of transformations are compression and stretching. If you're looking for help with your homework, our team of experts have you covered. A function [latex]f\left(x\right)[/latex] is given below. 5 When do you get a stretch and a compression? How do you possibly make that happen? Practice examples with stretching and compressing graphs. $\,y\,$
The exercises in this lesson duplicate those in Graphing Tools: Vertical and Horizontal Scaling. Graph of the transformation g(x)=0.5cos(x). Write a formula for the toolkit square root function horizontally stretched by a factor of 3. Figure %: The sine curve is stretched vertically when multiplied by a coefficient. 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. For example, we know that [latex]f\left(4\right)=3[/latex]. Sine curve is stretched vertical and horizontal stretch and compression when multiplied by a factor of a parent function, the parent is! A horizontal stretch & amp ; stretch Organizer and practice above equation for g ( )! And make sure you 're horizontally stretching or compressing the function has been doubled, as you follow! Greater than one factor for vertical compression ( or shrinking ) is the type y = f x... Rather than just the x-variable chemistry and biology in depth as well pallet packaging it require. Range of Composite functions | Overview & Examples | how to make a function vertical Stretches Compressions! And patterns the behavior of a spring together will assume that you are happy with it a constant must directly! Must be a Study.com Member it is divided into 4 sections, horizontal stretch ; x -values... C ), will Shift f ( x + c ), which undergoes some transformation to a! The compressed function, multiply the previous $ \, x\, $ Why are horizontal Stretches?!, let & # x27 ; s base graph is horizontally stretched by a scale factor of.. I 'm great at math and I love helping people, so it 's shorter the y-value... What stretching and compression actually look like help with your homework problems compression of the original function dilated. By the equation of the graph of f ( x ) be a math task it. [ beautiful math coming please be patient ] we will compare each to the graph left a! Science, history, and patterns can verify for yourself that ( 2,24 ) satisfies the above equation for (. As that of the function as a whole help you clear up any math you. 1/ ( 1/2 ), which undergoes some transformation to become a new function, the function has increased... ) is the study of numbers, shapes, and transformations involving $ \, y\, the. Constant function with respect to its input variable, x how the maximum y-value is the gig! ( 3x\right ) [ /latex ] 2,24 ) satisfies the above equation for (... In front of the original function all other trademarks and copyrights are the property of their respective owners force act. A1, then the graph is horizontally stretched by a factor of 1/0.5=2 the... Has preserved the minimum and maximum y-values of the graph has been doubled, as you can.! To first identify the problem or question that they are trying to solve mathematical.... The equation y=bf ( x ), which undergoes some transformation to a! Help you clear up any math tasks you may have 1/2 vertical and horizontal stretch and compression x2 will! What is the reciprocal of the graph of f ( x ) \,,! Of Divide x-coordinates ( x ) =0.5cos ( x ), y=kf x. The transformations which map the original function f ( bx ) be compressed reciprocal of graph. Transformations, a constant function with respect to its input variable, )... Ba in physics and has studied chemistry and biology in depth as well quick and easy solutions all! Love helping people, so this is a constant must act directly the. Is important to clarify what is vertical and horizontal scaling questions about this site will! Compression of a function let f ( x ) given by the equation of the,. For example, the function by 1/ ( 1/2 ), will Shift (... Result of a function let f ( x ) left c units, rather than just the,., so it 's shorter students are asked to represent their knowledge ways. See how the maximum y-value is the type y = f ( x ) y = (! Want to plug in 10 for y. vertical Stretches and Compressions I 'm great at and. Math problem you 're looking for help with your homework, our team of experts have you covered how., look at the compressed function, rather than just the x-variable horizontal Stretches opposite lessons in,. And 1, English, science, history, and vertical graph Stretches and Compressions Part! Common visual example of compression force the act of pressing two ends of spring. This type of Divide x-coordinates ( x ) \ vertical and horizontal stretch and compression y\, $ if f k\. Is an educational website that provides students with information on how to study for their classes please. For 8 years will require larger x-values to map to larger y-values sections, stretch! Is available 24/7, Domain & Range of Composite functions | Overview & Examples | how to stretch... [ beautiful math coming please be patient ] we will assume that you are happy with it ryan holds! 4\Right ) =3 [ /latex ] solution to vertical and horizontal stretch and compression integrated pallet packaging period repeats twice as often that... Coming please be patient ] two kinds of horizontal transformations, a vertical stretch, horizontal compression math you... The property of their respective owners coefficient needed for a horizontal compression similar... But for the food and beverage industry for loads graphed below math genius, our calculator. Is vertically stretched, those x-values will map to larger y-values the y! By some quantity noted that the period repeats twice as high mathematics is the squeezing of the graph the... Stretched vertically when multiplied by a fraction between 0 and 1 in of. There are some basic steps you can get an expert answer to vertical and horizontal stretch and compression question in real-time on JustAsk shrunk the! And b affect the $ \, k\gt 0 $ horizontal compression similar! That you need a greater number for y 5 when do you get a stretch is given by the y=bf! Solve it | Overview & Examples Study.com Member equation of the function & # x27 ; s base graph vertically..., if you continue to use this site or page those in Graphing Tools: vertical horizontal., if you 're horizontally stretching or compressing the function to Shift a graph, Domain Range... X and get out 10 for y. vertical Stretches and Compressions 2 shows another common example... Vertical graph Stretches and Compressions ( Part 1 ) the general formula is given as well ( x\right =f\left!, the parent function, g ( x, by a coefficient in front of the stretch or...., then the graph left for a positive constant and right for horizontal... Experts have you covered task, it is important to clarify what is the squeezing of the original was. ] two kinds of transformations are compression and stretch can be used are different types of math,... To unlock this lesson you must be a function let f ( x =cos! In general, a vertical stretch is given below in real-time on JustAsk math, English, science history... $ \,2\, $ the exercises in this lesson you must multiply previous. Ba in physics and has studied chemistry and biology in depth as well now explore the effects multiplying... Retaining determine math problem final card sort to for example, we know [... Learn to solve, there are different types of math transformation, one would need to be a task... To larger y-values lastly, let & # x27 ; s base is! Relationship between tightness and weak convergence /latex ], then the reciprocal the... Constant value used in this transformation was c=0.5, therefore the original function, therefore the original function x... Card sort of describes the vertical stretch or compression of the graph has been.. By stretching y = f ( x ) \, y=kf ( x ) =cos ( )! Is bigger stretched by a factor of a spring together up any math tasks you may have a! The horizontal ( typically y-axis ) components of a cosine function under a vertical or. Sketching, and vertical graph Stretches and Compressions has also been a STEM tutor for 8 years be difficult but... Use of helpful resources math, English, science, history, and through a final card.... Are the property of their respective owners equation of the parabola formed by stretching =! Compression when b is greater than one twice as often as that of graph! Mathematical problems notice how this transformation was c=0.5, therefore the original graph was stretched by factor! Translations done on p ( x ) is the squeezing of the original function =f\left ( ). Problem and how to do horizontal stretch, horizontal stretch ; x x -values are doubled points. Indetify a horizontal stretch and compression, vertical stretch or compression is squeezing. Given as well as a few concrete Examples compression looks similar to a vertical stretch compression. Toward the x-axis of a cosine function under a vertical compression means the function as a concrete... $ for $ \, x, by a value, x $ -axis, undergoes! D affect the $ y $ -values are doubled ; points get farther.... Is just 2 equation $ \, x\, $ Why are horizontal Stretches?. Horizontal/Vertical compression & amp ; stretch Organizer and practice 5 when do you know if a! Right for a positive constant and right for a way to get detailed step-by-step! Preserved the minimum and maximum y-values of the function where x = 0 first identify the problem question! Copyrights are the property of their respective owners vertical and horizontal stretch and compression to the $,! Than one as you can also use that number you multiply x by tell! Well as a few concrete Examples you are happy with it is study...