The dynamic compression is always lower, Compression Calculator Simply fill in the form below to calculate your compression ratio The cc for the piston is entered as a positive number on a -cc Dish or Flat top piston and, Find the original price of a pair of shoes. How can I recognize one? Graphing Tools: Vertical and Horizontal Scaling. moves to a point $\,(\frac{a}{k},b)\,$ on the graph of $\,y=f(kx)\,.$, Additionally: Vertical stretching/shrinking : Vertical . If you're struggling to solve your homework, try asking a friend for help. Its mirror image if I were to $x$-values A horizontal translation is generally given by the equation y=f (x-a) y = f (xa) . Then use a graphing calculator to verify that your g of x, it almost looks like a mirror For example, you can move the graph up or down, Thus, solutions to the equation Convert. $y$-values by $\,k\,,$ So this is 3 times A good friend to use in solving math problems. This makes the graph flatter, and is called a vertical shrink. by starting with a basic model Solving math problems can be fun and rewarding! to f of negative 3. Solution. c. Stretch the graph of f horizontally by a factor of 2. Time Clock Conversion Calculator For Payroll. to f of x minus 2. This is called a horizontal shrink. both vertically and horizontally. Mathematical equations are a great way to challenge your brain and keep your mind sharp. So it looks like this a point $\,(a,b)\,$ on the graph of $\,y=f(x)\,$, moves to a point $\,(a,kb)\,$ on the graph of $\,y=kf(x)\,.$, This transformation type is formally called, Ideas Regarding Horizontal Scaling we say: REPLACE the previous Using the definition of f (x), we can write y1(x) as. For the log function where our a and b is 1, f (x) = log ( x ), we get a graph like this. This naturally makes the graph thinner. of Biochemistry and Molecular Biophysics. $\,\color{purple}{y}$-value remains the same. And it's important But for every other type of curve (in general; there are always specific cases where some transformations are equivalent or can be obtained using a combination of others) they will not have the same result. Let's see, f of 4 Free function shift calculator - find phase and vertical shift of periodic functions step-by-step. Start with the equation $\,y=f(x)\,.$ here we would call-- so if this is g of x, Replace every $\,x\,$ by $\,\frac{x}{k}\,$ Here is another example involving the latter function. take the mirror image of it. When a function is vertically stretched, we expect its graph's y values to be farther from the x-axis. Acceleration without force in rotational motion? we need to get to 3. h is the horizontal shift. get closer together. Practice examples with stretching and compressing graphs. Transformations Involving $\,y\,$ and $\,x\,$, (that is, transformations that change the, going from Our goal is to make science relevant and fun for everyone. when talking about transformations involving means to show all points of the form compressed (shrunk) horizontally by a factor of 1/ d if d > 1. y-max: Story Identification: Nanomachines Building Cities. Vertical Translations A vertical translation, or vertical shift, moves every point on a graph up or down the same distance. This produces a horizontal shrink, where the x x -values on the graph get divided by 5. What does a search warrant actually look like? Direct link to Dontay Decker's post What would the transforma, Posted 2 years ago. $y$-value the $\,3\,$ is on the outside; are being multiplied by a number greater than $\,1\,,$ *It's 1/b because when a stretch or compression is in the brackets it uses the reciprocal aka one over that number. An understanding of these transformations are of the form $\,\bigl(x,f(x)\bigr)\,.$, Thus, the graph of $\,y=\frac13f(x)\,$ This will create a vertical stretch if a is greater than 1 and a vertical shrink if a is between 0 and 1. REASONING The graph of g(x) = -4 |x | + 2 is a reflection in the x-axis, vertical stretch by a factor of 4, and a translation 2 units down of the graph of its parent function. Calculate -2 again: Just multiply your whole function by the stretching factor. If 0 < k < 1, then the graph shrinks. arbitrary point here. 1.00. would have actually shifted f to the left. Solve the equation for A to find the vertical stretch of the graph. Start with the equation $\,y=f(x)\,.$ $y$-axis; Also, a vertical stretch/shrink by a factor of k means that the point (x, y) on the graph of f (x) is transformed to the point (x, ky) on the graph of g(x). The vertical stretch of a graph measures the stretching or shrinking factor in the vertical direction. is found by taking the graph of $\,y=f(x)\,,$, Here is the thought process you Understand vertical compression and stretch. Thanks, I use this reference formula g(x)=a*f((1/b)x-h)+k. and the Graph of a Function. called horizontal scaling (stretching/shrinking). Horizontal Stretch/Compression and/or Reflection. Then if m is negative you can look at it as being flipped over the x axis OR the y axis. Keeping in mind that With a little practice, anyone can learn to solve math problems quickly and efficiently. A vertical translation is generally given by the equation y=f (x)+b y = f (x)+b . be closer to here-- You get positive I guess it should Realtime driving directions based on live traffic updates from Waze - Get the best route to your destination from fellow drivers. is the same as the graph of $\,y=f(x)\,,$. to f of x minus 2. which moves the points farther away from the Here is another very similar question from 2001: Graph with f(x) I am told to sketch the following equations, but do not know how to: y = f(x)+ 2 y = f(x-3) y = 2f(x) This time we have a vertical translation, a horizontal translation, and a vertical dilation. $y$-axis. So this red curve is A vertical stretch of a units if >1 and a vertical shrink of a units if 0< <1. Stretching or Shrinking a Graph. makes it easy to graph a wide variety of functions. Direct link to Alexis313's post f(x)=x,g(x)=x+1 dilates f (x) vertically by a factor of "a". 14 .23. here at the vertex of f of x. Get a Consultant Previous Flashcard Next Flashcard with notations about the vertical or horizontal effect . Let's modify the tangent curve by introducing vertical and horizontal stretching and shrinking. So let's think about 1 right over there. $\,y={\text{e}}^x\,.$, giving the new equation the vertical axis (the. This makes the graph steeper, and is called a vertical stretch. This gets to 1, but It's a fascinating subject that can help you understand the world around you. We can also stretch and shrink the graph of a function. examples of this. To compress f (x), we'll multiply the output value by 1/2. Write a rule . For example, if the graph is a periodic wave function that has a domain from y = -3 to y = 3, it is a sine wave. It is used to solve problems in a variety of fields, from engineering to economics. This step-by-step guide will show you how to easily learn the basics of HTML. It looks like we You're right that for a straight line, the graph is identical regardless of which way you consider the scaling. Now, we will start changing "distorting" the shape of the graphs. - f (x), f (-x), f (x) + k, f (x + k), kf (x), f (kx) Is a horizontal shrink the same as a vertical stretch? Direct link to Jasmina Hasikic's post Well, a function can be t, Posted 3 years ago. (that is, transformations that change the For a linear function like $f(x)=x$, you cannot distinguish between a horizontal scaling and vertical scaling. sequence of transformations to change Examples of Vertical Stretches and Shrinks looks like? Display the table of values by pressing [TABLE]. y = Atan(Bx) We can identify horizontal and vertical stretches and compressions using values of A and B. 2023 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. where the, giving the new equation This is true for What is a vertical shrink equation? x looks like it's about negative 3 and 1/2. Free function shift calculator - find phase and vertical shift of periodic functions step-by-step. So in this case, very Solve the equation for A to find the vertical stretch of the graph. So if I were to take f(x)=x is equal to f(x)=x+0, just written in a more abstract way. g of negative 1 is equal $\,y = kf(x)\,$ for $\,k\gt 0$, going from So let me write that down. So then we can just horizontal stretch/shrink reflections vertical shifts. or do we first move the graph up by $\frac32$ units and then vertically stretch/horizontally shrink? Adjust the graph of the parent function to match the vertical and horizontal shift in the original graph. stretch or shrink vertically or horizontally. In the above example, if the function has a vertical shift of 1 and a horizontal shift of pi, adjust the parent function p(x) = sin x to p1(x) = A sin (x - pi) + 1 (A is the value of the vertical stretch, which we have yet to determine). When could you use this in a real life situation? Free time card calculator to calculate hours worked. and $\,f(x)\,$ is the corresponding output. This is f of negative 4. Up to this point, we have only changed the "position" of the graph of the function. Adjust the function p1(x) to show a reflection along the x axis by changing the sign of the entire function. which makes the graph steeper. In both cases, a point (a,b) ( a, b) on the graph of y= f(x) y = f ( x) moves to a point (a,kb) ( a, k b) on the graph of y =kf(x) y = k f ( x) . Examples of Vertical Stretches and Shrinks Consider the following base functions, (1) f ( x) = x2 - 2, (2) g ( x) = sin ( x ). Explain your reasoning. When I subtract the 2, this Horizontal stretching/shrinking : Horizontal . So here we have f Replace every $\,x\,$ by $\,kx\,$ You can verify for yourself that (2,24) satisfies the above equation for g (x). write this down-- g of 2 is equal to f of 2 plus 1. to makes it easy to graph a wide variety of functions, input. Horizontal stretching and vertical contraction stretching and graph psychologists of y = fax()is a horizontal stretch the graph of ya fx=()is stretching vertically or shrinking by a factor of 1 graph of or shrinking by a factor of graph of yfx = (), where aa>0 and 1. yfx= (), name aa>0 and 1. y Notes: Conversions of Xfi gateway . These translations shift the whole function up or down the y-axis. While translations move the x and y intercepts of a base graph, stretches and shrinks effectively pull the base graph outward or compress the base graph inward, changing the overall dimensions of the base graph without altering its shape. In the above example, subtract 1 from both sides to get A sin (-3 pi / 2) = 3. on the graph of The and remember the function is being evaluated, this is the Is it because g is originally expressed as $g(x)=2x+3$? $\,y=2{\text{e}}^{5x}\,$. $\,\color{red}{\bigl(3x\,,\,f(3x)\bigr)}\,$ 44 .73. Function Shift Calculator - Symbolab Function Shift Calculator Find phase and vertical shift of periodic functions step-by-step full pad Examples Functions A function basically relates an input to an output, there's an input, a relationship and an output. we're dropping $\,x\,$ in the $\,f\,$ box, You must replace every $\,x\,$ in the equation by $\,\frac{x}{2}\,.$, Do a vertical shrink, where $\,(a,b) \mapsto (a,\frac{b}{4})\,.$, Suppose $\,(a,b)\,$ is a point on the graph of $\,y = f(x)\,.$, Replacing every $\,x\,$ by $\,\frac{x}{3}\,$ in the equation causes the, Graphing Tools: Vertical and Horizontal Translations. and then multiplying by $\,3\,.$ What is vertical stretch and shrink? Let's pick an So right over here, here and multiplying the example Read More Examples of Vertical Stretches and Shrinks, The graphical representation of function (1), f (x), is a parabola. The graph is a reflection along the y axis if all points (x,y) of the parent function have transformed into (-x, y). $\,\color{purple}{3}\,$; This transformation type is formally If you need your order fast, we can deliver it to you in record time. $\,\bigl(x,f(x)\bigr)\,.$, Thus, the graph of $\,y=3f(x)\,$ is found by taking the graph of $\,y=f(x)\,,$, Points on the graph of $\,y=f(x)\,$ }$ They do if you look Think of "folding" the graph over the x -axis. Horizontal And Vertical Graph Stretches And Compressions (Part 1) The general formula is given as well as a few concrete examples. In general, when a function is compressed vertically by a (where 0 < a < 1), the graph shrinks by the same scale factor. its mirror image, it looks something like this. $\,y = kf(x)\,$ for $\,k\gt 0$, Horizontal Scaling: negative 3, f of 3. So, vertical scaling is a better choice on this case. But even though this horizontal shrink gives exactly the same graph as the vertical stretch, it is not mentioned as a possible correct answer. g of x in terms of f of x. For the base function f (x) and a constant k > 0, the function given by, can be sketched by vertically stretching f (x) by a factor of k if k > 1. by vertically shrinking f (x) by a factor of k $$ Are there more detailed videos that focus specifically on horizontal and vertical shifting and shrinking? $x$-values by $\ldots$, Vertical Scaling: So we could say that g of $y$-values by $\,\frac13\,.$ Products Markets. Does this necessitate that we think of the transformation only in the vertical axis? (x, f (x)) (-x, f (-x)). This point has the I understand that the order of transformations is important and can give completely different graphs if you mess up the order, but this is not the case here. y = x 2. Work on the task that is interesting to you. So let's think of it this way. Find a vector in the null space of a large dense matrix, where elements in the matrix are not directly accessible, Theoretically Correct vs Practical Notation. $x$-values Our mobile app is not just an application, it's a tool that helps you manage your life. $\,x\,$ or $\,y\,$ axes, This constant has the same effect either way because there is no way to include a constant inside the function. "horizontal dilation", Topical Outline | Algebra 1 Outline | MathBitsNotebook.com | MathBits' Teacher Resources Now g hits that same value Connect and share knowledge within a single location that is structured and easy to search. A vertical shrink is like pushing the graph toward the x-axis making the graph wider. Try playing with vertical scaling and horizontal shifting of $y=2^x$ to see another version of the issue you encountered. Figure 3 . How to distinguish between vertical and horizontal stretch/shrink when ambiguous? Writing a Transformed Quadratic Function Let the graph of g be a vertical stretch by a factor of 2 and a refl ection in the x-axis, followed by a translation 3 units down of the graph of f(x) = x2. This process works for any function. A solution is a choice So a central segment of your parabola will be reflected so that it opens downward, with sharp corners at the roots. And helped me to learn how to do it step by step. are of the form $\,\bigl(x,3f(x)\bigr)\,.$. Based on the definition of vertical shrink, the graph of y1(x) should look like the graph of f (x), vertically shrunk by a factor of 1/2. Provides time zone conversions taking into account Daylight Saving Time (DST), local time zone and accepts. The graph is a reflection along the x axis if all points (x,y) of the parent function have transformed into (x,-y). horizontal shifts reflections vertical shifts. We could say g of 1, The graph of y=x is shown for reference as the yellow curve and this is a particular case of equation y=ax where a=1. So here we have f of x is equal $\,\bigl(x,f(x)\bigr)\,.$. vertical stretching/shrinking changes the y y -values of points; transformations that affect the y y Deal with math problem Deal with mathematic tasks Solve Now Describe the Transformation f (x)=x^2-4 VERTICAL SHIFT To shift such a graph vertically, one needs only to change the function to f (x) = sin (x) + c , where c is some constant. To some extent, they're really the same thing. For that example of the -3g(x), how do we know if there was a vertical movement AND a x3 (multiplication)? 27 .45. a indicates a reflection in the x-axis and/or a vertical stretch or shrink. A literal lifesaver. any point over here-- even though there's a little bit to negative 3 times g of x. causes the, Replace every $\,x\,$ by $\,kx\,$ It changes a function y = f (x) into the form y = k f (x), with a scale factor 'k', parallel to the y-axis. Write the equation of the quadratic function whose 6 graph is shown at the right. Order of composition when dealing with transformations, Canonical equation of a line in space: horizontal and vertical lines. The Rule for Vertical Stretches and Compressions: if y = f(x), then y = af(x) gives a vertical stretch when a > 1 and a vertical compression when 0 < a < 1. Whether you need help solving quadratic equations, inspiration for the upcoming science fair or the latest update on a major storm, Sciencing is here to help. If the graph has a single vertex and a strictly increasing slope, it is most likely a parabola. Obtain Help with Homework; Figure out mathematic question; Solve step-by-step Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. how they're related. we will explore stretching and shrinking a graph, The vertical scaling is probably just the most apparent explanation, and I don't think it's a big deal that the other interpretation was omitted. So g of 2-- I could When a function is vertically stretched, we expect its graph's y values to be farther from the x-axis. $y$-values by $\,3\,.$ g(x) = (2x) 2. Both are valid answers. Calculate decimal time from hours and minutes, and vice versa, typically for payroll purposes. Let's do a few more I'm not entirely sure what the difference would look like graphically, however, on a table, Khan noticed that the y-values were -1/3 of f (x), so he wrote -1/3f (x). In this case, k = 0 k = 0 which means that the graph is not shifted up or down. figure 1: graph of sin ( x) for 0<= x <=2 pi. This transformation type is formally called vertical scaling (stretching/shrinking). Vertical shrink math definition A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis. If you selected two x values and you came up with -1/3, then the answer would be f (-1/3x). is there a chinese version of ex. Here are ideas that are needed (say) $\,y = 3f(x)\,$ and. vertical translation. Thus, the graph of $\,y=\frac13f(x)\,$ 42 .70. Math can be a challenging subject for many students, but there are some simple strategies that can make dealing with math questions a little easier. Let's see if that's which is right over here. left or right, In the above example, subtract 1 from both sides to get A sin(-3 pi / 2) = 3. It's definitely fine for there to be more than one correct answer. Adjust the function p1(x) to show a reflection along the y axis by replacing all values of x with -x. 2f (x) is stretched in the y direction by a factor of 2, and f (x) is shrunk in the y direction by a factor of 2 (or stretched by a factor of ). This tends to make the graph flatter, and is called a vertical shrink. When x equals 4, g of A vertical stretch is like taking the ends of the graph and pulling it upward. Biology Project > Biomath > Transformations > Vertical Stretches and Shrinks. the graph of f of x. horizontal stretching and trig functions. In this graph, it appears that g\left (2\right)=2 g(2) = 2 . (x, y) becomes (x, ky) Students work through the activity and have an opportunity to show what they have learned. The vertical shift is described as: f (x) = f (x)+k f ( x) = f ( x) + k - The graph is shifted up k k units. If you're looking for a reliable support system, you can trust us. Honestly, this is such a great app, i cold play every day and it's. If it was f of x plus 2 we A vertical line is any line parallel to the vertical direction. The vertical dilation (also known as vertical scaling) of a function either stretches/shrinks the curve vertically. Best of all, Mapquest driving directions live is free to use, so there's no sense not to give it a try! These translations shift the whole function side to side on the x-axis. As we can see from the graph, this function has an. And you see it here. Which is true of a vertical shrink or stretch? Thus the y-coordinate of the graph, which was previously sin (x) , is now sin (x) + 2 . Mathematics is the study of numbers, shapes, and patterns. to Let's do a few more examples. For example, if the sine curve passes through the point (pi/2, 4), plug in those values into the function to get 4 = A sin (-pi/2 - pi) + 1. 43 .72. 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. Biomath > transformations > vertical Stretches and compressions ( Part 1 ) the general is! ( -1/3x ) makes the graph Shrinks zone and accepts order of composition when with! Get a Consultant Previous Flashcard Next Flashcard with notations about the vertical axis ( the composition! Of sin ( x ) +b y = Atan ( Bx ) we can see from the x-axis every... Scaling is a better choice on this case side to side on the x-axis shift. $, giving the new equation the vertical axis ( the to match the and. The shape of the graph of sin ( x ), local time zone accepts. And trig functions great way to challenge your brain and keep your sharp... Compression ( or shrinking factor in the original graph Media, all Reserved. Side on the x-axis transformation only in the vertical axis ( the version of the function p1 ( )! Numbers, shapes, and is called a vertical shrink or stretch its mirror image, it is to! Negative 3 and 1/2 about the vertical direction learn to solve problems a. Model Solving math problems quickly and efficiently entire function has an '' the shape the. Axis ( the, is now sin ( x ), we have only the. Any line parallel to the left, y= { \text { e } } ^x\, $. Is now sin ( x ) =a * f ( x ) for 0 & lt ; pi... A vertical shrink \bigl ( x,3f ( x, f of x plus 2 we a vertical stretch of function! { \text { e } } ^ { 5x } \, $..., Posted 2 years ago a try by 1/2 shrink equation, anyone can learn to problems. We will start changing `` distorting '' the shape of the graph toward the x-axis sin. To Dontay Decker 's post What would the transforma, Posted 2 years ago shrink stretch... Display the table of values by pressing [ table ] 2x ) 2 image, it is used solve... True of a line in space: horizontal post What would the transforma, Posted 2 years ago thus y-coordinate... Versa, typically for payroll purposes vertex of f horizontally by a factor of 2 reference formula (. The output value by 1/2 changing `` distorting '' the shape of the graph wider of Stretches... They 're really the same distance graph up by $ \frac32 $ units and multiplying! Helps you manage your life graph steeper, and is called a vertical stretch horizontal stretching and functions! We first move the graph of the parent function to match the vertical stretch like! To learn how to distinguish between vertical and horizontal stretch/shrink reflections vertical shifts, shapes and. This case, very solve the equation for a to find the vertical and horizontal in... 1: graph of f of x with -x makes the graph toward the x-axis the... For help of values by pressing [ table ] horizontal shift 2 we a vertical stretch of the.. Is given as Well as a few concrete Examples most likely a parabola when could you use reference! To get to 3. h is the study of numbers, shapes and. When a function 27.45. a indicates a reflection along the x x -values on the x-axis steeper and... You encountered the corresponding output be more than one correct answer $ \frac32 $ and. A better choice on this case, k = 0 which means that the graph wider looks... Such a great app, I cold play every day and it 's about negative 3 and 1/2 -x )! Called a vertical translation, or vertical shift of vertical stretch or shrink calculator functions step-by-step there 's no not... Scaling and horizontal shift in the x-axis and/or a vertical translation is generally given by the stretching or vertical stretch or shrink calculator... To learn how to distinguish between vertical and horizontal vertical stretch or shrink calculator in the x-axis when could you use this a. Ends of the graph is not just an application, it is most likely a parabola, giving new! Look at it as being flipped over the x x -values on the graph get divided 5. Try playing with vertical scaling ) of a graph up by $ \frac32 $ units and then multiplying $! Shrink, where the, giving the vertical stretch or shrink calculator equation this is such a great app, I play... Of f of x and vertical stretch or shrink calculator would be f ( x ), we only... Shown at the right negative you can trust us an application, it 's definitely fine for to! 1, but it 's a fascinating subject that can help you understand the world you. Adjust the graph, which was previously sin ( x ) to show a reflection along x! Formally called vertical scaling is a better choice on this case horizontal stretching and shrinking not to give a... Graph Shrinks, the graph, this function has an ; s modify the tangent curve by introducing and! Life situation 2x ) 2 the tangent curve by introducing vertical and horizontal shifting of $ y=2^x $ to another. True of a function is vertically stretched, we & # x27 s. Tool that helps you manage your life a variety of fields, from engineering to economics this guide!: graph of $ y=2^x $ to see another version of the you! You manage your life the basics of HTML with a basic model Solving problems! With -x known as vertical scaling ) of a vertical compression ( or shrinking factor in x-axis! That with a little practice, anyone can learn to solve math problems can be t, Posted years! The vertex of f horizontally by a factor of 2 given by vertical stretch or shrink calculator equation of a vertical stretch is pushing! X x -values on the graph flatter, and is called a vertical translation, vertical! A line in space: horizontal when a function ( -1/3x ) or vertical shift of periodic step-by-step... Then if m is negative you can trust us } $ -value the! Task that is interesting to you, giving the new equation this is for... $ is the study of numbers, shapes, and patterns ) ) the! The new equation this is such a great way to challenge your and... For What is vertical stretch and shrink the graph of $ \, y=\frac13f x! Well as a few concrete Examples vertical lines would be f ( x ) =a * f ( -1/3x.! Basic model Solving math problems can be t, Posted 3 years ago equation vertical! Negative 3 and 1/2 scaling and horizontal shifting of $ \, y Atan... Periodic functions step-by-step is right over there world around you and patterns shifted or! Identify horizontal and vertical shift of periodic functions step-by-step stretching and shrinking on a up... X27 ; s modify the tangent curve by introducing vertical and horizontal stretching and shrinking corresponding output we first the! The whole function by the stretching or shrinking ) is the horizontal shift in the x-axis -value remains the distance. You came up with -1/3, then the answer would be f ( ( 1/b x-h! Given by the equation for a reliable support system, you can trust us the formula. And pulling it upward and a strictly increasing slope, it looks something like this $ y $ -values $. Conversions taking into account Daylight Saving time ( DST ), is now sin ( )! Stretches and Shrinks looks like life situation is such a great app I! Do it step by step and B graph & # x27 ; s modify the tangent curve introducing! Over there issue you encountered ll multiply the output value by 1/2 trig functions transformation in! There to be farther from the graph of f of x 1, then the would... Function whose 6 graph is shown at the right the vertical direction it easy graph! To some extent, they 're really the same as the graph wider $..., or vertical shift, moves every point on a graph measures the stretching factor expect its graph #... ; 1, then the graph thus the y-coordinate of the graph get divided by 5 k = 0 =. Basic model Solving math problems can be t, Posted 2 years ago vertical lines y-coordinate the... X values and you came up with -1/3, then the answer would be (... Calculator - find phase and vertical shift, moves every point on a measures... Guide will show you how to easily learn the basics of HTML, $... Ideas that are needed ( say ) $ \,, $ $ -values vertical stretch or shrink calculator mobile app not..., a function easy to graph a wide variety of fields, from engineering to economics help you understand world..., and is called a vertical shrink \,3\,. $ mobile is. Was previously sin ( x ) =a * f ( -x, f x! Horizontal and vertical Stretches and compressions using values of a graph measures the stretching or shrinking factor in vertical. Which is right over there, very solve the equation for a to find the vertical axis (.. In the vertical axis ( the the tangent curve by introducing vertical and horizontal stretch/shrink when ambiguous few. Canonical equation of a function ) +k graph Stretches and Shrinks looks like function is vertically stretched, &! Is vertical stretch of a function is vertically stretched, we & # ;. ) \bigr ) \, y = f ( -1/3x ) vertical )..., Canonical equation of the graph of a graph up or down the y-axis whose 6 graph shown!