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Describing Transformations of Absolute Value Functions

Describing Transformations of Absolute Value Functions 1.13 - Solution

Let's graph $g(x)$ first and then we can compare it to the graph of the parent function, $f(x)=|x|.$

Graphing $g(x)$

To graph the function, let's make a table of values first!

$x$ $2\left|x\right|$ Simplify $g(x)$
${\color{#0000FF}{\text{-}3}}$ $2\left|{\color{#0000FF}{\text{-}3}}\right|$ $2(3)$ $6$
${\color{#0000FF}{\text{-}2}}$ $2\left|{\color{#0000FF}{\text{-}2}}\right|$ $2(2)$ $4$
${\color{#0000FF}{\text{-}1}}$ $2\left|{\color{#0000FF}{\text{-}1}}\right|$ $2(1)$ $2$
${\color{#0000FF}{0}}$ $2\left|{\color{#0000FF}{0}}\right|$ $2(0)$ $0$
${\color{#0000FF}{1}}$ $2\left|{\color{#0000FF}{1}}\right|$ $2(1)$ $2$
${\color{#0000FF}{2}}$ $2\left|{\color{#0000FF}{2}}\right|$ $2(2)$ $4$
${\color{#0000FF}{3}}$ $2\left|{\color{#0000FF}{3}}\right|$ $2(3)$ $6$

Now we can plot these ordered pairs on a coordinate plane and connect them to get the graph of $g(x).$ Notice that $g(x)$ is a transformation of $f(x)$ and the graph of $f(x)=|x|$ is V-shaped. Thus, $g(x)$ will also be a V-shaped graph.

Comparing the Functions

To compare our graph to the graph $f(x)=|x|,$ let's draw them on one coordinate plane.

As we can see, the graph of $g(x)$ is a vertical stretch of the graph $f(x)$ by a factor of $2.$