Choose the best answer.

Which is the correct piecewise definition for the function [tex] y = |x + 5| - 2 [/tex]?

A. [tex] y = x + 3 [/tex] for [tex] x < -5 [/tex] and [tex] y = -7 [/tex] for [tex] x \geq -5 [/tex]

B. [tex] y = x - 3 [/tex] for [tex] x < 5 [/tex] and [tex] y = -x + 7 [/tex] for [tex] x \geq 5 [/tex]

C. [tex] y = x + 3 [/tex] for [tex] x > -5 [/tex] and [tex] y = -x + 7 [/tex] for [tex] x < -5 [/tex]

D. [tex] y = x - 3 [/tex] for [tex] x \geq 5 [/tex] and [tex] y = -x + 7 [/tex] for [tex] x \geq 5 [/tex]

Question

High School

Answer :

shashankvt shashankvt · Answer 1 · 2023-12-14T13:29:15-05:00

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.

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.

learn more about piecewise functions here :

https://brainly.com/question/28225662

#SPJ9