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

C

Step-by-step 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