# What is the graph of the absolute value function f(x) = 4 | x | – 2?

Dec 29, 2017

The graph of $f \left(x\right)$ is the standard "V" graph of $\left\mid x \right\mid$ scaled by 4 units and shifted 2 units negative ("down") on the $y -$axis.

#### Explanation:

$f \left(x\right) = 4 \left\mid x \right\mid - 2$

Let's first consider the "parent" graph $y = \left\mid x \right\mid$

This is the standard "V" graph shown below:

graph{absx [-10, 10, -5, 5]}

Now, $f \left(x\right)$ is this standard graph scaled by 4 units and shifted 2 units negative ("down") on the $y -$axis. As below:

graph{4absx-2 [-10, 10, -5, 5]}