# How do you graph f(x)= -3 abs(x -2)?

May 23, 2018

See below

#### Explanation:

$f \left(x\right) = - 3 \cdot \left\mid x - 2 \right\mid$

Consider the the standard graph of $y = \left\mid x \right\mid$ below.

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

Then, $f \left(x\right)$ has this standard graph shifted 2 units positive (right) on the $x -$axis and scaled by 3 units.

graph{3abs(x-2) [-10, 10, -5, 5]}

Then reflected in the $x -$axis. As below,

graph{-3abs(x-2) [-10, 10, -5, 5]}