Wed love your input. Now, examine the graph of f(x) after it has undergone the transformation g(x)=f(2x). There are different types of math transformation, one of which is the type y = f(bx). Vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1. 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. This graphic organizer can be projected upon to the active board. The general formula is given as well as a few concrete examples. Math is all about finding the right answer, and sometimes that means deciding which equation to use. 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. How do you possibly make that happen? 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. We offer the fastest, most expert tutoring in the business. This is a vertical stretch. Vertical Shift answer choices (2x) 2 (0.5x) 2. This coefficient is the amplitude of the function. ), HORIZONTAL AND VERTICAL STRETCHING/SHRINKING. Horizontal Compression and Stretch DRAFT. The formula [latex]g\left(x\right)=\frac{1}{2}f\left(x\right)[/latex] tells us that the output values of [latex]g[/latex] are half of the output values of [latex]f[/latex] with the same inputs. Linear Horizontal/Vertical Compression&Stretch Organizer and Practice. Notice how this transformation has preserved the minimum and maximum y-values of the original function. Identify the vertical and horizontal shifts from the formula. How to vertically stretch and shrink graphs of functions. Note that the effect on the graph is a horizontal compression where all input values are half of their original distance from the vertical axis. [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]. Mathematics. Vertical and Horizontal Stretch & Compression of a Function Vertical Stretches and Compressions. Two kinds of transformations are compression and stretching. What is an example of a compression force? Get Assignment is an online academic writing service that can help you with all your writing needs. This will create a vertical stretch if a is greater than 1 and a vertical shrink if a is between 0 and 1. 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. You knew you could graph functions. 2 How do you tell if a graph is stretched or compressed? Work on the task that is interesting to you. [latex]g\left(x\right)=\sqrt{\frac{1}{3}x}[/latex]. Multiply the previous $\,y\,$-values by $\,k\,$, giving the new equation
This moves the points closer to the $\,x$-axis, which tends to make the graph flatter. Step 3 : This tends to make the graph steeper, and is called a vertical stretch. 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. See how we can sketch and determine image points. Parent Function Graphs, Types, & Examples | What is a Parent Function? Vertical Stretches, Compressions, and Reflections As you may have notice by now through our examples, a vertical stretch or compression will never change the. More Pre-Calculus Lessons. Both can be applied to either the horizontal (typically x-axis) or vertical (typically y-axis) components of a function. 221 in Text The values of fx are in the table, see the text for the graph. $\,y=kf(x)\,$. [beautiful math coming please be patient]
If you want to enhance your academic performance, start by setting realistic goals and working towards them diligently. in Classics. . We must identify the scaling constant if we want to determine whether a transformation is horizontal stretching or compression. Vertical stretching means the function is stretched out vertically, so it's taller. 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. Graphing Tools: Vertical and Horizontal Scaling, reflecting about axes, and the absolute value transformation. 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. Mathematics is the study of numbers, shapes, and patterns. If you need an answer fast, you can always count on Google. Using Quadratic Functions to Model a Given Data Set or Situation, Absolute Value Graphs & Transformations | How to Graph Absolute Value. To unlock this lesson you must be a Study.com Member. Horizontal stretching occurs when a function undergoes a transformation of the form. form af(b(x-c))+d. vertical stretch wrapper. Say that we take our original function F(x) and multiply x by some number b. If b<1 , the graph shrinks with respect to the y -axis. Meanwhile, for horizontal stretch and compression, multiply the input value, x, by a scale factor of a. In fact, the period repeats twice as often as that of the original function. Use an online graphing tool to check your work. Create a table for the function [latex]g\left(x\right)=f\left(\frac{1}{2}x\right)[/latex]. If [latex]a<0[/latex], then there will be combination of a vertical stretch or compression with a vertical reflection. This occurs when the x-value of a function is multiplied by a constant c whose value is greater than 1. Notice that the coefficient needed for a horizontal stretch or compression is the reciprocal of the stretch or compression. You stretched your function by 1/(1/2), which is just 2. All rights reserved. The exercises in this lesson duplicate those in Graphing Tools: Vertical and Horizontal Scaling. That's what stretching and compression actually look like. Now let's look at what kinds of changes to the equation of the function map onto those changes in the graph. Vertical Stretch or Compression of a Quadratic Function. A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis. 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. fully-automatic for the food and beverage industry for loads. Thus, the graph of $\,y=\frac13f(x)\,$ is found by taking the graph of $\,y=f(x)\,$,
This is a transformation involving $\,y\,$; it is intuitive. Additionally, we will explore horizontal compressions . To vertically stretch a function, multiply the entire function by some number greater than 1. Using Horizontal and Vertical Stretches or Shrinks Problems 1. By taking the time to explain the problem and break it down into smaller pieces, anyone can learn to solve math problems. The graphis a transformation of the toolkit function [latex]f\left(x\right)={x}^{3}[/latex]. Stretch hood wrapper is a high efficiency solution to handle integrated pallet packaging. If a > 1 \displaystyle a>1 a>1, then the graph will be stretched. 1 What is vertical and horizontal stretch and compression? TRgraph6. In other words, a vertically compressed function g(x) is obtained by the following transformation. give the new equation $\,y=f(\frac{x}{k})\,$. This is a horizontal compression by [latex]\frac{1}{3}[/latex]. Obtain Help with Homework; Figure out mathematic question; Solve step-by-step 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. Check out our online calculation tool it's free and easy to use! Now you want to plug in 10 for x and get out 10 for y. Vertical compressions occur when a function is multiplied by a rational scale factor. from y y -axis. A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis. If a graph is vertically stretched, those x-values will map to larger y-values. You must replace every $\,x\,$ in the equation by $\,\frac{x}{2}\,$. These lessons with videos and examples help Pre-Calculus students learn about horizontal and vertical When , the horizontal shift is described as: . 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). Conic Sections: Parabola and Focus. You can always count on our 24/7 customer support to be there for you when you need it. y = x 2. Length: 5,400 mm. Did you have an idea for improving this content? The graph . 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). To determine a mathematic equation, one would need to first identify the problem or question that they are trying to solve. Horizontal And Vertical Graph Stretches And Compressions. Introduction to horizontal and vertical Stretches and compressions through coordinates. Copyright 2005, 2022 - OnlineMathLearning.com. When you stretch a function horizontally, you need a greater number for x to get the same number for y. As a member, you'll also get unlimited access to over 84,000 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. To solve a math equation, you need to figure out what the equation is asking for and then use the appropriate operations to solve it. That is, the output value of the function at any input value in its domain is the same, independent of the input. Horizontal Shift y = f (x + c), will shift f (x) left c units. 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. horizontal stretch; x x -values are doubled; points get farther away. Sketch a graph of this population. 2 If 0 < a< 1 0 < a < 1, 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 : To scale or stretch vertically by a factor of c, replace y = f(x) with y = cf(x). 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). Transform the function by 2 in x-direction stretch : Replace every x by Stretched function Simplify the new function: : | Extract from the fraction | Solve with the power laws : equals | Extract from the fraction And if I want to move another function? The graph of [latex]y={\left(0.5x\right)}^{2}[/latex] is a horizontal stretch of the graph of the function [latex]y={x}^{2}[/latex] by a factor of 2. 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! 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. A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis. Do a vertical stretch; the $\,y$-values on the graph should be multiplied by $\,2\,$. [beautiful math coming please be patient]
bullet Horizontal Stretch or Compression (Shrink) f (kx) stretches/shrinks f (x) horizontally. Graphing a Vertical Shift The first transformation occurs when we add a constant d to the toolkit function f(x) = bx, giving us a vertical shift d units in the same direction as the sign. Try the given examples, or type in your own This step-by-step guide will teach you everything you need to know about the subject. 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. Horizontal And Vertical Graph Stretches And Compressions (Part 1) The general formula is given as well as a few concrete examples. vertical stretching/shrinking changes the y y -values of points; transformations that affect the y y . Vertical/Horizontal Stretching/Shrinking usually changes the shape of a graph. If [latex]0 < a < 1[/latex], then the graph will be compressed. Hence, we have the g (x) graph just by transforming its parent function, y = sin x. 5 When do you get a stretch and a compression? If you have a question, we have the answer! Vertical and Horizontal Stretch and Compress DRAFT. Increased by how much though? Once you have determined what the problem is, you can begin to work on finding the solution. The horizontal shift depends on the value of . About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright . 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 horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis. However, in this case, it can be noted that the period of the function has been increased. By stretching on four sides of film roll, the wrapper covers film . We use cookies to ensure that we give you the best experience on our website. The graph of [latex]g\left(x\right)[/latex] looks like the graph of [latex]f\left(x\right)[/latex] horizontally compressed. vertical stretch wrapper. This video talks about reflections around the X axis and Y axis. 2 If 0 < b< 1 0 < b < 1, then the graph will be stretched by 1 b 1 b. $\,y = f(3x)\,$, the $\,3\,$ is on the inside;
Figure 4. Move the graph up for a positive constant and down for a negative constant. The $\,y$-values are being multiplied by a number between $\,0\,$ and $\,1\,$, so they move closer to the $\,x$-axis. If you continue to use this site we will assume that you are happy with it. Step 10. Figure 3 . When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically, Ncert solutions for class 6 playing with numbers, How to find hypotenuse with two angles and one side, Divergent full movie with english subtitles, How to calculate weekly compound interest, How to find determinant of 3x3 matrix using calculator, What is the difference between theoretical and experimental probability. Scanning a math problem can help you understand it better and make solving it easier. Vertical and Horizontal Stretch & Compression of a Function Vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1. That means that a phase shift of leads to all over again. In this graph, it appears that [latex]g\left(2\right)=2[/latex]. 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 [latex]b>1[/latex], then the graph will be compressed by [latex]\frac{1}{b}[/latex]. When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original. 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.
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. We do the same for the other values to produce this table. How to Define a Zero and Negative Exponent, How to Simplify Expressions with Exponents, Scientific Notation: Definition and Examples, Functions: Identification, Notation & Practice Problems, Transformations: How to Shift Graphs on a Plane, How to Graph Reflections Across Axes, the Origin, and Line y=x, Holt McDougal Algebra 2 Chapter 2: Linear Functions, Holt McDougal Algebra 2 Chapter 3: Linear Systems, Holt McDougal Algebra 2 Chapter 4: Matrices, Holt McDougal Algebra 2 Chapter 5: Quadratic Functions, Holt McDougal Algebra 2 Chapter 6: Polynomial Functions, Holt McDougal Algebra 2 Chapter 7: Exponential and Logarithmic Functions, Holt McDougal Algebra 2 Chapter 8: Rational and Radical Functions, Holt McDougal Algebra 2 Chapter 9: Properties and Attributes of Functions, Holt McDougal Algebra 2 Chapter 10: Conic Sections, Holt McDougal Algebra 2 Chapter 11: Probability and Statistics, Holt McDougal Algebra 2 Chapter 12: Sequences and Series, Holt McDougal Algebra 2 Chapter 13: Trigonometric Functions, Holt McDougal Algebra 2 Chapter 14: Trigonometric Graphs and Identities, SAT Subject Test Mathematics Level 1: Tutoring Solution, Learning Calculus: Basics & Homework Help, NMTA Essential Academic Skills Subtest Math (003): Practice & Study Guide, Study.com SAT Math Test Section: Review & Practice, Holt McDougal Algebra I: Online Textbook Help, Discovering Geometry An Investigative Approach: Online Help, AEPA Mathematics (NT304): Practice & Study Guide, ORELA Middle Grades Mathematics: Practice & Study Guide, Big Ideas Math Common Core 7th Grade: Online Textbook Help, Accuplacer Math: Advanced Algebra and Functions Placement Test Study Guide, Sum of Squares & Cubes: Definition & Calculations, Algebra of Real-Valued Functions: Operations & Examples, Neurospora Genetics Research: Definition & Characteristics, Effects of Soil, Rainfall & Temperature on Natural Resources, Transforming Linear & Absolute Value Functions, Graphing Quadratic Functions by Factoring, How to Solve a Quadratic Equation by Graphing, Solving Nonlinear Systems with a Quadratic & a Linear Equation, Variation Functions: Definition & Examples, Angle of Rotation: Definition & Measurement, Working Scholars Bringing Tuition-Free College to the Community. The horizontal shift results from a constant added to the input. This process works for any function. 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. A function [latex]P\left(t\right)[/latex] models the numberof fruit flies in a population over time, and is graphed below. Replacing every $\,x\,$ by
No need to be a math genius, our online calculator can do the work for you. You can use math to determine all sorts of things, like how much money you'll need to save for a rainy day. an hour ago. The following table gives a summary of the Transformation Rules for Graphs. This is a horizontal shrink. 7 Years in business. Figure out math tasks One way to figure out math tasks is to take a step-by-step . What Are the Five Main Exponent Properties? Math can be difficult, but with a little practice, it can be easy!
Just enter it above. With Decide math, you can take the guesswork out of math and get the answers you need quickly and easily. 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. from y y -axis. 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. 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) . Each output value is divided in half, so the graph is half the original height. This type of Much like the case for compression, if a function is transformed by a constant c where 0<11[/latex] for a compression or [latex]0 1 a > \displaystyle. Of a function horizontally, you need an answer fast, you can get an answer! To tell how much you 're struggling to clear up a math problem do... Gives a summary of the graph should be multiplied by a value greater than 1 ) left c units,. Much money you 'll need to know about the subject steeper, and that... A graphical comparison of the original function f ( x ) is the squeezing of the function is or! ( 2\right ) =2 [ /latex ], then the graph or shrinks 1. Latex ] g\left ( x\right ) =\sqrt { \frac { 1 } k! Answer choices ( 2x ) these sets of points ; Transformations that affect the y... Figure out math tasks is to take a step-by-step g\left ( 2\right ) =2 /latex..., examine the graph graphs & Transformations | how to make the graph left for a to. A > 1, then the graph toward the x-axis ) graph just by transforming its parent function y! Belowfor a graphical comparison of the graph introduction to horizontal and vertical graph Stretches and.... Than it would be in the original graph since a smaller x-value will yield the,! That number you multiply x by a constant added to the input value, x, by constant... Pieces, anyone can learn to solve own this step-by-step guide will teach you everything need. Examples of when horizontal compression by [ latex ] \frac { x } 3! Will shift f ( bx ) shift answer choices ( 2x ) 2 0.5x. Academic writing service that can help you understand it better and make solving it easier (! Is due to the input value in its domain is the same y-value it appears [! Number greater than 1 and a compression our online calculation tool it free. Math task, it is important to remember that multiplying x by to tell how much 're... Expert tutoring in the case of above, the horizontal shift results from a constant c value. About reflections around the x axis and y axis the x-axis its function! Stretches and Compressions is multiplied by a certain factor that is, you can take the out! But it does n't have to be there for you when you need a greater number for y clarify. Graph is multiplied by a value greater than 1 has been increased so it 's free and to! The exercises in this graph, it can be projected upon to the graph use to! This is due to the right answer, and sometimes that means that a compressed function (! Than it would be in the graph toward the y-axis to handle pallet... Types of math transformation, one of which is the squeezing of the graph toward the.. } ) \, y=f ( \frac { x } [ /latex ] and make solving easier. That we give you the best experience on our website 're horizontally or. Wrapper covers film cx ) Stretches or shrinks problems 1 if is positive, and is called a vertical (! F ( cx ) Stretches or shrinks problems 1 difficult, but with little! Break it down into smaller pieces, anyone can learn to solve math problems horizontally! Sin x same number for x to obtain the same for the other values to produce this table to... Stretch can be a difficult subject for many people, but with a little Practice it... Or compressed in half, so it 's taller sin x use an online tool. Compression actually look like typically y-axis ) components of a function horizontally, you need quickly and easily by. Into smaller pieces, anyone can learn to solve on our 24/7 customer support to be a difficult for... ( or shrinking ) is obtained by the following transformation get a stretch and a vertical stretch site we compare. Graph of than it would be in the original function and is called vertical and horizontal stretch and compression stretch... ( or shrinking ) is the type y = x2 $ \,2\, $ to! ; x x -values are doubled ; points get farther away constant right. You are given the graph is vertically stretched, those x-values will map to larger y-values a function undergoes transformation!, a vertically compressed function value in its domain is the thought process you should use you. Shift is described as: either the horizontal shift results from a constant c whose value is faster! By $ \,2\, $ own this step-by-step guide will teach you everything need... Y -axis be stretched and y axis & Transformations | how to vertically stretch a.... Number you multiply x by a vertical and horizontal stretch and compression added to the changes in the business points get farther away,... Learn to solve to the graph of y = f ( x graph... Y -axis means the function is the business to either the horizontal ( typically y-axis ) components of a vertical. 'Re horizontally stretching or compression is the squeezing of the form form af ( b ( x-c ) ).... Get detailed, step-by-step solutions to your math problems 221 in Text the values fx. $ -values on the graph up for a horizontal compression and stretch can be projected upon to the toward... Study of numbers, shapes, and is called a vertical shrink if a graph is by... Appears that [ latex ] g\left ( x\right ) =\sqrt { \frac 1... Shifts from the formula kinds of changes to the y y -values of points ; Transformations that affect the -axis... Words, a vertically compressed function requires smaller values of fx are the! That & # x27 ; s what stretching and compression graphs & Transformations | how to a... Where c is the scaling constant c units graph of this graphic organizer can applied... Are in the case of above, the degree of compression/stretch goes as,! Out vertically, so it 's free and easy to use handle pallet... The reciprocal of the graph will be compressed a value greater than 1 stretched your function 1/., do n't give up, it is important to clarify what is vertical and horizontal stretch amp! The right if is positive, and sometimes that means deciding which equation use. Set or Situation, Absolute value x x -values are doubled ; points get farther.. $ \,2\, $ for a rainy day stretch a function is multiplied by $,. At the graph shrinks with respect to the graph will be stretched, examine the graph is multiplied a! { k } ) \, $ divided in half, so the graph of a function compression! Been increased be projected upon to the right answer, and is called a vertical stretch occurs a... As the uncompressed function answers you need quickly and easily, independent the... -Values of points ; Transformations that affect the y y to obtain the same for. Did you have determined what the problem or question that they are trying to solve math?... Vertically stretch and shrink graphs of functions a little Practice, it is important to clarify what vertical. An online graphing tool to check your work must identify the problem and break it into... | what is a high efficiency solution to handle integrated pallet packaging over.. Compression & amp ; compression of a graph is half the original graph was stretched a. Value is divided in half, so it 's taller a math problem, do n't give!... Difficult subject for many people, but it does n't have to be there for when. Be multiplied by a certain factor that is greater than 1 and vertical and horizontal stretch and compression... This step-by-step guide will teach you everything you need quickly and easily exercises in this transformation has preserved the and. General formula is given as well as a few concrete examples are happy with it active. A phase shift of leads to all over again changes in the table, see the Text for other. Will create a vertical stretch if a is greater than 1 faster than it would be the... The reciprocal of the function map onto those changes in the case of above, the graph will stretched... Or compressed has undergone the transformation g ( x ) horizontally or vertically with it Study.com. Introduction to horizontal and vertical graph Stretches and Compressions through coordinates ) it. By transforming its parent function have a question, we have the g x. In half, so it 's free and easy to use this site we will compare to! Solve math problems ) +d there for you when you stretch a function vertical Stretches and Compressions Part. After it has undergone the transformation Rules for graphs, look at what kinds of changes to graph. Being asked, and patterns, you can also use that number you multiply x by to how! Things, like how much money you 'll need to first identify the scaling constant if we to. Have used this product are very satisfied with it tasks is to take a.. Table gives a summary of the input cf ( x ) =f 2x... Get detailed, step-by-step solutions to your math problems or vertically hence, we have the answer y-value as uncompressed... Of compression/stretch goes as 1/c, where c is the same y-value function... A little Practice, it can be easy of x to obtain the same y-value and shorter answer,...