Question

If a function is reflected vertically and has the range y ∈ ℝ | -50 < y < 50, why does this reflection not affect its range?

a) The reflection only affects the domain
b) The reflection preserves the distance between the function values
c) The range is symmetric, so the reflection doesn't change it
d) Reflecting vertically always expands the range

Answer 1

The reflection of a function vertically does not affect its range because the range is symmetric.

Step-by-step explanation:

The correct answer is c) The range is symmetric, so the reflection doesn't change it.

When a function is reflected vertically, its graph is flipped across the x-axis. This reflection does not affect the range because the range represents the set of all possible output values of the function. Since the reflection is symmetric about the x-axis, the original range remains the same.

For example, if the original function had a range of y ∈ ℝ | -50 < y < 50, the reflected function will also have the same range.