# How do you graph y =2 abs(x-4)+ 1?

Jul 22, 2015

Graph the domain for $\left(x - 4\right) \le 0$ and then the domain for $\left(x - 4\right) \ge 0$

#### Explanation:

Note that the two components are both linear, so only 2 points are required for each.

For $\left(x - 4\right) \le 0$
$\textcolor{w h i t e}{\text{XXXX}}$if $x = 4 \rightarrow y = 2 \left\mid 0 \right\mid + 1 = 1$
$\textcolor{w h i t e}{\text{XXXX}}$if $x = 0 \rightarrow y = 2 \left(\left\mid - \right\mid 4\right) + 1 = 9$

For $\left(x - 4\right) \ge 0$
$\textcolor{w h i t e}{\text{XXXX}}$if $x = 4 \rightarrow y = 2 \left\mid 0 \right\mid + 1 = 1$
$\textcolor{w h i t e}{\text{XXXX}}$if $x = 8 \rightarrow y = 2 \left\mid 4 \right\mid + 1 = 9$