Given this...... (algebra 2 help)

Question

Given f(x) =  3x if x > 0

                    x-2 if x ≤ 0

 

which is the rule for g(x), a vertical translation of f(x) 4 units down?

 

A) g(x)= 3x-12 if x > 0

             x-6 if x ≤ 0

 

B) g(x)= 3x-4 if x > -4

              x-6 if x ≤ -4

 

C) g(x)= 3x-4 if x > 0

              x-6 if x ≤ 0

 

D) g(x)= 3x+4 if x > 0

              x-2 if x ≤ 0

Answer 1

Translations work the same for piece-wise functions as they do for other functions. A vertical translation 4 units down means you should replace f(x) with g(x) = f(x) - 4:

 

g(x) = f(x) - 4 = 3x - 4 if x > 0

                         = x - 6 if x ≤ 0

 

That's answer choice (C).