Question

What is the effect on the graph of the function f(x) = x when f(x) is replaced with −f(x)?

A) shifts down 1 unit
B) shifts left 1 unit
C) vertical reflection over x-axis
D) horizontal reflection over y-axis

Answer 1

C

Explanation:

Lets review some transformation rules. Let function be f(x). So:

• f(x+b) is the parent shifted b units left horizontally
• f(x-b) is the parent shifted b units right horizontally
• f(x) + a is the parent shifted a units up vertically
• f(x) - a is the parent shifted a units down vertically
• -f(x) is a vertical reflection across x-axis
• f(-x) is a horizontal reflection across y-axis

Now, on to our question. We want to find what happens to parent function [f(x)] if we were to write it like [-f(x)].

From the rules, we see that it is the second last one. This means it is a vertical reflection over the x-axis.

From the answer choices, the correct choice is C