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

Aug 17, 2015

With absolutes you usually make two graphs.

#### Explanation:

(1)
When $x \ge - 2 \to x + 2 \ge 0$ so the absolute bars don't have to come into action, and the equation simplifies to:
$f \left(x\right) = x + 2 + 3 = x + 5$

(2)
When $x < - 2 \to x + 2 < 0$ and the bars flip the sign into
$f \left(x\right) = - \left(x + 2\right) + 3 = - x + 1$

These two graphs meet at $\left(- 2 , 3\right)$
graph{|x+2|+3 [-16.35, 15.68, -1.93, 14.09]}