The graph of the polynomial function f, where y = f(x), has x-intercep (May 2023 U.S.)

Correct answer: A. f (-6) = 0.
o determine which of the given statements must be true, we need to analyze the properties of the polynomial function f(x) based on the given x-intercepts.
The x-intercepts of a polynomial function are the values of x where the function is equal to 0. In this case, the x-intercepts are (-6, 0) and (6, 0).

Let's evaluate each of the given statements:
A. f(-6) = 0
This statement is true. Since (-6, 0) is an x-intercept, it means that f(-6) = 0.
B. f(6) = -6
This statement is false. The x-intercept (6, 0) means that f(6) = 0, not -6.
C. f(-6) = 6
This statement is false. The x-intercept (-6, 0) means that f(-6) = 0, not 6.
D. f(0) = -6
This statement is false. The x-intercepts are at (-6, 0) and (6, 0), but there is no information given about the value of the function at x = 0.

Therefore, the only statement that must be true is option A: f(-6) = 0.