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

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.

Lie

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