# How do you graph the equation y=|x+2|+3?

##### 1 Answer
Dec 19, 2014

The absolute value changes of sign, when it's content $< 0$.
So let's write that down:
$x + 2 < 0 \iff x < - 2$
So now we know that it will change the sign (negative) when $x < - 2$
It's best to treat a function with an absolute value as two functions.

• $x > - 2 \implies y = x + 2 + 3 \iff y = x + 5$
• $x < - 2 \implies y = - \left(x + 2\right) + 3 \iff y = - x - 2 + 3 \iff y = - x + 1$

See how I added the minus sign when $x < - 2$?

If you now graph both of these functions on one graph, you will have your function. You do have to remember that the first function only exists when $x > - 2$, and that the second function only exists when $x < - 2$.