# Horizontal stretch and compression equation

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Feb 4, 2013 - This video explains to graph graph horizontal and vertical stretches and compressions in the form a*f(b(x-c))+d. This video looks at how a and b affect the g... Horizontal Stretching and Compression of Graphs This applet helps you explore the changes that occur to the graph of a function when its independent variable x is multiplied by a positive constant a (horizontal stretching or compression). The Rule for Horizontal Stretches and Compressions: if y = f(x), then y = f(bx) gives a horizontal stretch when 0 < b < 1 and a horizontal compression when b > 1. Note that unlike translations where there could be a more than one happening at any given time, there can be either a horizontal stretch or a vertical compression but not both at the same time. As you may have notice by now through our examples, a vertical stretch or compression will never change the $$x$$ intercepts. This is a good way to tell if such a transformation has occurred. Example 261 In the above function, if we want to do horizontal expansion or compression by a factor of "k", at every where of the function, "x" co-ordinate has to be multiplied by the factor "k". Then, we get the new function y = f (kx) The graph of y = f (kx) can be obtained by expanding or compressing the graph of y = f (x) horizontally by the factor "k". Stretching a graph involves introducing a coefficient into the function, whether that coefficient fronts the equation as in y = 3 sin(x) or is acted upon by the trigonometric function, as in y = sin(3x). Though both of the given examples result in stretches of the graph of y = sin(x), they are stretches of a certain sort. The first example ... Well let's think about it. If it was multiplying by just a positive 2.5, you would stretch it out. At each point it would go up by a factor of 2 and 1/2. But it's a negative 2.5, so at each point, you're going to stretch it out and then you're going to flip it over the x-axis. So let's do that. So when x was 0, you got 1 in this case. Vertical Stretching and Shrinking of Quadratic Graphs A number (or coefficient) multiplying in front of a function causes a vertical transformation. Vertical Stretching and Shrinking are summarized in the following table: Horizontal translations: Translation right h units Translation left h units Combined horizontal and vertical Reflection in x -axis Stretch Shrink Shrink/stretch with reflection Vertex form of Absolute Value Function I get mixed up with vertical and horizontal compressions/stretches when it comes to looking at the equation. If the equation isY= .25(Xsquared), is that a horizontal stretch/compression or vertical stretch/compression? If the equation is Y=2(Xsquared), which of those is it? If the equation is Y=(.25X)squared, which is it? Stretching a graph involves introducing a coefficient into the function, whether that coefficient fronts the equation as in y = 3 sin(x) or is acted upon by the trigonometric function, as in y = sin(3x). Though both of the given examples result in stretches of the graph of y = sin(x), they are stretches of a certain sort. The first example ... According to your post, we want "a horizontal stretch by a factor of 1/2." Since stretches and compressions are inverses, we know that a stretch by a factor of 1/2 is the same as a compression by a factor of 2. The quoted portion of the linked page tells us that, to get a compression of a factor of k, we need a k greater than 1. Hence, k must be 2. I get mixed up with vertical and horizontal compressions/stretches when it comes to looking at the equation. If the equation isY= .25(Xsquared), is that a horizontal stretch/compression or vertical stretch/compression? If the equation is Y=2(Xsquared), which of those is it? If the equation is Y=(.25X)squared, which is it? “horizontal shift to the right (left) by _____ units” “vertical stretch/compression by a factor of _____” “horizontal stretch/compression by a factor of _____” 11. Given the graph of the function f(x) shown below. Graph each of the given transformations. Practice Problems: Pg 216: 8,10,28 Pg 223: 3,5,19 C > 1 stretches it; 0 < C < 1 compresses it We can stretch or compress it in the x-direction by multiplying x by a constant. g(x) = (2x) 2. C > 1 compresses it; 0 < C < 1 stretches it; Note that (unlike for the y-direction), bigger values cause more compression. We can flip it upside down by multiplying the whole function by −1: g(x) = −(x 2) Find a possible equation for the common logarithmic function graphed in Figure $$\PageIndex{21}$$. Figure $$\PageIndex{21}$$ Solution. This graph has a vertical asymptote at $$x=–2$$ and has been vertically reflected. We do not know yet the vertical shift or the vertical stretch. We know so far that the equation will have form: I get mixed up with vertical and horizontal compressions/stretches when it comes to looking at the equation. If the equation isY= .25(Xsquared), is that a horizontal stretch/compression or vertical stretch/compression? If the equation is Y=2(Xsquared), which of those is it? If the equation is Y=(.25X)squared, which is it? The equations used to make the stretch and compression are: and . Which equation do you think goes with which graph? If you guessed that the red graph is and the blue graph is then you are correct. Now, based on this can you make generalizations about vertical stretches and compressions? Well let's think about it. If it was multiplying by just a positive 2.5, you would stretch it out. At each point it would go up by a factor of 2 and 1/2. But it's a negative 2.5, so at each point, you're going to stretch it out and then you're going to flip it over the x-axis. So let's do that. So when x was 0, you got 1 in this case. 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. Given a function $y=f\left(x\right)$, the form $y=f\left(bx\right)$ results in a horizontal stretch or compression. Identify a horizontal or vertical stretch or compression of the function f(x) = √x by observing the equation of the function g(x)= 1/8 √x . A) A horizontal stretch by a factor of √1/8 B) A vertical compression by a factor of 8 C) A horizontal compression by a factor of 8 D) A vertical stretch by a factor of √1/8 Sep 14, 2013 · introduction to horizontal stretches and compressions and reflections over the y-axis 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. Given a function $y=f\left(x\right)$, the form $y=f\left(bx\right)$ results in a horizontal stretch or compression. Feb 4, 2013 - This video explains to graph graph horizontal and vertical stretches and compressions in the form a*f(b(x-c))+d. This video looks at how a and b affect the g... Vertical stretch and reflection. The graph of y=ax² can be stretched by changing the value of a; in addition, a negative value of a will reflect the curve along the x-axis. Exercise: Vertical Stretch of y=x². The graph of y=x² is shown for reference as the yellow curve and this is a particular case of equation y=ax² where a=1. Nov 10, 2019 · Often when given a problem, we try to model the scenario using mathematics in the form of words, tables, graphs, and equations. One method we can employ is to adapt the basic graphs of the toolkit … Q. Which equation has a horizontal stretch, vertical compression, shift left and shift down? Stretching a graph involves introducing a coefficient into the function, whether that coefficient fronts the equation as in y = 3 sin(x) or is acted upon by the trigonometric function, as in y = sin(3x). Though both of the given examples result in stretches of the graph of y = sin(x), they are stretches of a certain sort. The first example ... The equations used to make the stretch and compression are: and . Which equation do you think goes with which graph? If you guessed that the red graph is and the blue graph is then you are correct. Now, based on this can you make generalizations about vertical stretches and compressions? Figure 274 Explore the properties of horizontal stretches and compressions discussed in this section with this applet. You can change the base function $$f(x)$$ using the input box and see many different stretches/compressions of $$f(x)$$ by moving around the $$a$$ slider. Subsection Exercises 1 Exploring Horizontal Compressions and Stretches Q. Which equation has a horizontal stretch, vertical compression, shift left and shift down? Sep 14, 2013 · introduction to horizontal stretches and compressions and reflections over the y-axis