Question

Let g(x) be the reflection of f(x) in the x-axis. What is the function rule for g(x)?

Let g(x) be the reflection of f(x) = 3x + 12 in the x-axis. What is a function rule for g(x)?

A. g(x) = -3x + 12
B. g(x) = 3x + 12
C. g(x) = 3x - 12
D. g(x) = -3x - 12

Answer 1

To reflect over the x axis (horizontal axis), multiply f(x) by -1. Use parenthesis to indicate -1 is multiplied by all of f(x) and not just a portion of it.

g(x) = -1*f(x)
g(x) = -1*( f(x) )
g(x) = -1*( 3x+12) 
g(x) = -1*(3x) - 1*(12)
g(x) = -3x - 12

Don't forget to distribute the negative to EVERY term inside the parenthesis. 

So the final answer is choice D.

Answer 2

The answer is D. g(x)=-3x-12