Describing Transformations of Absolute Value Functions

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 $2.$

Describing Transformations of Absolute Value Functions 1.13 - Solution

Graphing g(x)g(x)g(x)

Comparing the Functions

Graphing $g(x)$