# How do you graph  y= 3abs(x-4)- 2 ?

Jun 10, 2015

You take a look at the expression $x - 4$

#### Explanation:

For $x \ge 4 \to x - 4 \ge 0$ and the absolute bars leave it like that.

So the function is $y = 3 \left(x - 4\right) - 2 = 3 x - 14$

For $x < 4 \to x - 4 < 0$ the bars reverse the sign to make it positive

So the function becomes $y = 3 \left(4 - x\right) - 2 = - 3 x + 10$

These two should meet at $x = 4 \to y = 3 \cdot 0 - 2 = - 2$
graph{3|x-4|-2 [-4.75, 15.25, -3.04, 6.96]}