Question

Find g(x), where g(x) is the reflection across the y-axis of f(x) = -2(x - 5)² - 5.

A. g(x) = -2(x + 5)² - 5
B. g(x) = 2(x + 5)² - 5
C. g(x) = -2(x - 5)² + 5
D. g(x) = 2(x - 5)² + 5

Answer 1

The correct reflection of the function f(x) = -2(x - 5)² - 5 across the y-axis is g(x) = -2(x + 5)² - 5.

Step-by-step explanation:

To find the reflection of the function f(x) = -2(x - 5)² - 5 across the y-axis, we need to replace x with -x in the function. This is because reflecting a function across the y-axis changes the sign of the x-coordinates while leaving the y-coordinates unchanged.

Therefore, the reflection of f(x) across the y-axis, or g(x), is obtained by substituting x with -x:

g(x) = -2(-x - 5)² - 5

However, when you square -x - 5, the negative sign inside the parentheses gets squared as well, leaving the expression unchanged from (x + 5)². So the correct reflection of the function is:

g(x) = -2(x + 5)² - 5