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Answer :
The correct piecewise definition for the function y = |x + 5| - 2 is,
y = x + 3, for x ≥ -5 and y = - x - 7, for x < - 5.
What is an absolute value function?
We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.
In piecewise terms | x | = x for x ≥ 0 and | x | = - x for x < 0.
Given, y = | x + 5 | - 2.
Now, y = (x + 5) - 2, for x + 5 ≥ 0 and y = - (x + 5) - 2, for x + 5 < 0.
y = x + 3, for x ≥ -5 and y = - x - 7, for x < - 5.
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