The range of the polynomial function f is the set of real numbers less than or equal to 4. If the zeros of f are −3 and 1, which of the following could be the graph of y = f (x) in the xy-plane?

Options

A.
B.
C.
D.

Answer

A

Explanation

Since zeros of f correspond to the x-intercepts of the graph of f, and the range of f gives all the possible y-values on the graph of the function, the correct graph of the function has only points with y-values less than or equal to 4, and crosses the x-axis at only (−3, 0) and (1, 0). The graph in choice A satisfies both of these conditions.
Choice B is incorrect. The graph of the function matches the range given, but the zeros are at −1 and 3, not −3 and 1. Choice C is incorrect. The graph has y-values greater than 4. Choice D is incorrect. Even though the graph has zeros at −3 and 1, it has an additional zero at 0, and the range of the graph is the set of all real numbers. .