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# Describing Transformations of Absolute Value Functions

## Describing Transformations of Absolute Value Functions 1.6 - Solution

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

### Graphing $g(x)$

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

$x$ $\left|x\right|-5.5$ Simplify $g(x)$
${\color{#0000FF}{\text{-}5}}$ $\left|{\color{#0000FF}{\text{-}5}}\right|-5.5$ $5-5.5$ $\text{-}0.5$
${\color{#0000FF}{\text{-}3}}$ $\left|{\color{#0000FF}{\text{-}3}}\right|-5.5$ $3-5.5$ $\text{-}2.5$
${\color{#0000FF}{\text{-}1}}$ $\left|{\color{#0000FF}{\text{-}1}}\right|-5.5$ $1-5.5$ $\text{-}4.5$
${\color{#0000FF}{0}}$ $\left|{\color{#0000FF}{0}}\right|-5.5$ $0-5.5$ $\text{-}5.5$
${\color{#0000FF}{1}}$ $\left|{\color{#0000FF}{1}}\right|-5.5$ $1-5.5$ $\text{-}4.5$
${\color{#0000FF}{3}}$ $\left|{\color{#0000FF}{3}}\right|-5.5$ $3-5.5$ $\text{-}2.5$
${\color{#0000FF}{5}}$ $\left|{\color{#0000FF}{5}}\right|-5.5$ $5-5.5$ $\text{-}0.5$

Now we can plot these ordered pairs on a coordinate plane and connect them to get the graph of the parent function, $f(x)=|x|.$ 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 translation $5.5$ units down of the graph $f(x).$