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Describing Transformations of Absolute Value Functions

Describing Transformations of Absolute Value Functions 1.11 - Solution

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The graphs of f(x)=xf(x)=|x| and g(x)=axg(x)=a|x| both have vertices located at the origin, so we know that there haven't been any translations. However, g(x)g(x) is somewhat shrunk. This means aa is less than 1.1. a<1\begin{gathered} a < 1 \end{gathered} To get from the graph of f(x)f(x) to the graph of g(x),g(x), we need to shrink ff away from the yy-axis. Let's look at a point on each graph with the same yy-values and compare their xx-values.

As we can see from the graph, when the xx-value of g(x)g(x) is three times the xx-value of f(x),f(x), the yy-value is the same for both functions. Therefore, to get g(x),g(x), f(x)f(x) must be vertically shrunk by a factor of a=13.a=\frac{1}{3}.