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

D

Explanation:

I will outside some translation and reflection rules below:

Let a function be f(x)

Then,

• f(x) + a is the function shifted a units up
• f(x) - a is the function shifted a units down
• f(x-b) is the function shifted b units right
• f(x+b) is the function shifted b units left

Now, reflection:

• f(-x) is the original reflected across y-axis
• -f(x) is the original reflected in x-axis

It says to replace f(x) with f(-x), according to our rules, it is:

horizontal reflection over y-axis, answer choice D.

If you take a function f(x) = x + 2, then make f(-x), it becomes:

f(-x) = -x + 2

Graphing, you will see that they are reflections over y-axis. (graph attached).

Note:

f(x) is red

f(-x) is blue

So, answer choice is D