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# Graphing Absolute Value Functions

## Graphing Absolute Value Functions 1.10 - Solution

In order to decide for what values of $x$ the function $y=|x|-3$ is increasing and decreasing, we will make a table of values.

$x$ $y=|x|-3$
$\text{-}4$ $1$
$\text{-}3$ $0$
$\text{-}2$ $\text{-} 1$
$\text{-}1$ $\text{-} 2$
$0$ $\text{-} 3$
$1$ $\text{-} 2$
$2$ $\text{-} 1$
$3$ $0$
$4$ $1$

In the table of values we can see that for the negative values of $x,$ as $x$ increases, the function decreases. For the positive values of $x,$ as $x$ increases, the function increases. This we can write as follows. \begin{aligned} x<0: \quad &\text{the function decreases} \\ x>0: \quad &\text{the function increases} \end{aligned}