# How do you write the original function as a piecewise function y= -3* abs(x+1)+4?

Jul 6, 2018

$f \left(x\right) = \left\{\begin{matrix}3 x + 7 & \textcolor{w h i t e}{\text{XX}} & x \le - 1 \\ - 3 x + 1 & \null & x > - 1\end{matrix}\right.$

#### Explanation:

Given: $y = - 3 \cdot | x + 1 | + 4$

The absolute value function always has a positive answer. The quantity inside the absolute value can be both positive or negative. This means there are two possible equations:

$y = - 3 \left(x + 1\right) + 4 = - 3 x - 3 + 4$

$y = - 3 x + 1$

$y = - 3 \left(- 1\right) \left(x + 1\right) + 4 = 3 \left(x + 1\right) + 4$

$y = 3 x + 3 + 4$

$y = 3 x + 7$

The vertex of the absolute value occurs when the quantity in the absolute value $= 0$:

$x + 1 = 0 \implies \ast x = - 1 \ast$

Piecewise function is

$f \left(x\right) = \left\{\begin{matrix}3 x + 7 & \textcolor{w h i t e}{\text{XX}} & x \le - 1 \\ - 3 x + 1 & \null & x > - 1\end{matrix}\right.$