How do you graph y=2abs(x-3)+5?

Jul 7, 2015

Graph $y = 2 x - 1$ for all points with $x \ge 3$
and $y = 11 - 2 x$ for all points with $x \le 3$

Explanation:

Note that the y intercept at $\left(x , y\right) = \left(0 , 5\right)$ is valid for both line segments.

Pick an arbitrary value of $x > 3$ (for example $x = 4$)
then when $x \ge 3$ the line goes through
$\textcolor{w h i t e}{\text{XXXX}}$$\left(4 , 2 \left\mid 4 - 3 \right\mid + 5\right) = \left(4 , 7\right)$
Draw a line segment from $\left(0 , 5\right)$ through $\left(4 , 7\right)$

Pick an arbitrary value of $x < 3$ (for example $x = 2$)
then when $x \le 3$ the line goes throuhg
$\textcolor{w h i t e}{\text{XXXX}}$$\left(2 , 2 \left\mid 2 - 3 \right\mid + 5\right) = \left(2 , 7\right)$
Draw a line segment from $\left(0 , 5\right)$ through $\left(2 , 7\right)$

The resultant graph should look something like: