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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
<u>for (x+1) < 0</u>
y = -7.5(x +1) -5 = -7.5x -12.5
<u>for (x+1) ≥ 0</u>
y = 7.5(x +1) -5 = 7.5x +2.5
This means we can write the piecewise function as ...