Question

Which represents the reflection of f(x)=x over the x-axis?

A. f(x)=−x
B. f(x)=0
C. f(x)=1
D. f(x)=2

Answer 1

The reflection of the function f(x) = x over the x-axis is represented by f(x) = -x. This transformation inverts the y-values of the function, flipping the graph across the x-axis.

Step-by-step explanation:

The reflection of a function f(x) = x over the x-axis involves changing the sign of the output values of the function. To reflect the graph over the x-axis, we multiply the function by -1 which changes the sign but not the absolute value of each y-coordinate. Hence, the reflection of f(x) = x over the x-axis would be f(x) = -x.

This transformation essentially 'flips' the graph of the given function across the x-axis. If we had a point on the graph of the original function at (3, 3), the reflected point would be at (3, -3). Therefore, of the given options, A. f(x) = -x represents the reflection of the function f(x) = x over the x-axis