Question

If f(x) is a third degree polynomial function and g(x) = f(–2x), which of the following is NOT true?

f(x) and g(x) have the same x-intercepts.
f(x) and g(x) have the same y-intercepts.
f(2) = g(–1)
f(x) and g(x) have the same number of zeros

Answer 1

f(x) and g(x) have the same x-intercepts (is not true)

Explanation:

g(x) is a reflection across the y-axis and a horizontal compression of f(x). In general those transformations will move the x-intercepts. (The y-intercept and the number of x-intercepts will remain unchanged.)

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Comment on the question/answer

f(x) = x^3 is a 3rd degree polynomial. When transformed to g(x) = -8x^2, its only x-intercept (x=0) remains the same. The answer above will not apply in any instance where the only x-intercept is on the line of reflection. (The question is flawed in that it does not make any exception for such functions.)