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

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Mathematics

21 September, 22:21

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

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Answers (1)

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Liberty · Answer 1

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

Step-by-step 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

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

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