Answer:
- -7.5x -12.5, x < -1
- 7.5x +2.5, x ≥ -1
Step-by-step explanation:
The absolute value function changes slope at its vertex. Here, that vertex is translated to x = -1. To the left of that point, the function is equivalent to one that negates its argument:
|x| = -x . . . for x < 0
|x| = x . . . for x ≥ 0
for (x+1) < 0
y = -7.5(x +1) -5 = -7.5x -12.5
for (x+1) ≥ 0
y = 7.5(x +1) -5 = 7.5x +2.5
This means we can write the piecewise function as ...
[tex]y=\begin{cases}-7.5x-12.5,&\text{if }x<-1\\7.5x+2.5,&\text{if }x\ge-1\end{cases}[/tex]
