# For h(x)=abs[x]; how do you find h(-4),h(4),and h(-3)?

Sep 1, 2015

$h \left(- 4\right) = h \left(4\right) = 4$
$h \left(- 3\right) = 3$

#### Explanation:

Your function $h \left(x\right)$ is defined as the absolute value of $x$, written as $| x |$, which will always return a positive values regardless of the sign of $x$.

$\textcolor{b l u e}{| x | = \left\{\begin{matrix}x \text{ & " "if " x >=0 \\ -x" & " "if } x < 0\end{matrix}\right.}$

So, to find $h \left(- 4\right)$, simply replace $x$ with $\left(- 4\right)$. Since $\left(- 4\right) < 0$, the absolute value function will return

$h \left(- 4\right) = | - 4 | = - \left(- 4\right) = \textcolor{g r e e n}{4}$

For $h \left(4\right)$, you have $x = 4$, and since $4 \ge 0$, the absolute value function will return

$h \left(4\right) = | 4 | = \textcolor{g r e e n}{4}$

The function returned the same value for both $\left(- 4\right)$ and $4$. For $h \left(- 3\right)$ you have $\left(- 3\right) < 0$, so the function will return

$h \left(- 3\right) = | - 3 | = - \left(- 3\right) = \textcolor{g r e e n}{3}$