Question

If f(x) is a third degree polynomial function and g(x) = f(2x) + 2, which of the following must be true?

f(x) and g(x) have the same x-intercepts.
f(x) and g(x) have the same y-intercepts.
f(x) and g(x) have the same number of zeros.
f(0) = g(0) – 2

Answer 1

Choice D) which is f(0) = g(0) - 2

Explanation:

Plug x = 0 into the g(x) function to find that....

g(x) = f(2*x) + 2

g(0) = f(2*0) + 2 .... replace every x with 0

g(0) = f(0) + 2

g(0) - 2 = f(0) + 2 - 2 .... subtract 2 from both sides

g(0) - 2 = f(0)

f(0) = g(0) - 2