In the xy-plane, the graph of function f has x-intercepts at -3, -1, and 1. Which of the following could define f ?

Options

A. `f(x)=(x-3)(x-1)(x+1)`
B. `f(x)=(x-3)(x-1)^(2)`
C. `f(x)=(x-1)(x+1)(x+3)`
D. `f(x)=(x+1)^(2)(x+3)`

Answer

C

Explanation

All of the given choices are polynomials. If the graph of a polynomial function f in the xy-plane has an x-intercept at b, then (x − b) must be a factor of f(x). Since −3, −1, and 1 are each x-intercepts of the graph of f, it follows that (x + 3), (x +1), and (x − 1) must each be a factor of f(x). The factored polynomial function in choice C is the only polynomial given with these 3 factors.
Choices A, B, and D are incorrect because they do not contain all three factors that must exist if the graph of the polynomial function f has x-intercepts at −3, −1, and 1.