Question

Find g(x), where g(x) is the reflection across the x-axis of f(x)=|x|. Write your answer in the form a|x–h|+k, where a, h, and k are integers.

Answer 1

The reflection across the x-axis of the function f(x) = |x| is found by changing the sign of the y-values resulting in g(x) = -|x|. This can be simplified as g(x) = -1 * |x - 0| + 0.

Step-by-step explanation:

The reflection across the x-axis of the function f(x) = |x| can be found by changing the sign of the y-values. So, to find g(x), we can rewrite the absolute value function as g(x) = -|x|.

This can be further simplified as g(x) = -1 * |x|, where a = -1, h = 0, and k = 0. Therefore, the reflection of f(x) = |x| across the x-axis can be written as g(x) = -1 * |x - 0| + 0.