Question

Rewrite the equation y = -2 |x + 4| - 6 as two linear functions with restricted domains.

a) f(x) = -2x - 6, g(x) = 2x - 6
b) f(x) = 2x - 6, g(x) = -2x - 6
c) f(x) = -2x + 6, g(x) = 2x + 6
d) f(x) = 2x + 6, g(x) = -2x + 6

Answer 1

To rewrite the equation y = -2 |x + 4| - 6 as two linear functions with restricted domains, we can separate the absolute value function into two cases: when the expression inside the absolute value is positive and when it is negative. Case 1: When x + 4 ≥ 0, the linear function is f(x) = -2x - 14. Case 2: When x + 4 < 0, the linear function is g(x) = 2x + 4.

Step-by-step explanation:

To rewrite the equation y = -2 |x + 4| - 6 as two linear functions with restricted domains, we need to separate the absolute value function into two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: When x + 4 ≥ 0, the equation becomes y = -2 (x + 4) - 6. Simplifying this gives us y = -2x - 8 - 6, which can be written as the linear function f(x) = -2x - 14.

Case 2: When x + 4 < 0, the equation becomes y = -2 -(x + 4) - 6. Simplifying this gives us y = -2 + 2x + 8 - 6, which can be written as the linear function g(x) = 2x + 4.