Question

The graph of the even function f(x) has five x-intercepts. If (6, 0) is one of the intercepts, which set of points can be the other x-intercepts of the graph of f(x)? (–6, 0), (–2, 0), and (0, 0) (–6, 0), (–2, 0), and (4, 0) (–4, 0), (0, 0), and (2, 0) (–4, 0), (–2, 0), and (0, 0)

Answer 1

(0,0) (-6,0), (-2,0)

Explanation:

Answer 2

The correct choice is A. (-6,0), (-2,0) and (0,0).

Explanation:

Consider the provided information:

The provided function f(x) is an even function and has 5 x-intercept.

Therefore,

f(x) = f(-x)

Thus, there will be positive and negative pairs of zeros.

As it is given that the x intercept is at (6,0). Therefore, the another x intercept will be on (-6,0).

If there are an odd number of intercepts and function is even then, (0,0) will be the x intercept because of its own negation.

The only choice with (-6,0) and (0,0) is A.

Therefore, the correct choice is A. (-6,0), (-2,0) and (0,0).