Question

"Which absolute value function, when graphed, represents the parent function, f(x) = |x|, reflected over the x-axis?"

Which absolute value function represents the parent function reflected over the x-axis?

a) f(x) = -|x|
b) f(x) = ||x||
c) f(x) = |x| + 1
d) f(x) = |x - 1|

Answer 1

Option A. f(x) = -|x| is the absolute value function that represents the parent function reflected over the x-axis.

How is it so?

Let's analyze how the reflection over the x-axis works:

The parent function is f(x) = |x|, and to reflect it over the x-axis, you multiply the function by -1.

If we take f(x) = |x| and multiply it by -1, we get:

f(x) = -|x|

Considering the fact that;

1. For positive values of x, |-x| is the same as |x|, so it remains positive.

2. For negative values of x, |-x| becomes |x|, and then multiplying by -1 makes it negative.

So, the function f(x) = -|x| represents the reflection of the parent function f(x) = |x| over the x-axis.