Question

The graph of the even function F(X) Has 5 x-intercepts if (6,0) is the one of the intercepts what set of points can be the other intercepts of the graph of f(x)?

A.(-6,0) , (-2,0) ,and (0,0)
b.(-6,0) , (-2,0) , and (4,0)
c.(-4,0) , (0,0) , and (2,0)
d.(-4,0) , (-2,0) , and (0,0)

Answer 1

A

Explanation:

Answer 2

f(x) being even means

f(x) = f(-x)

So the zeros come in positive and negative pairs. If there are an odd number of intercepts like there are here, it's because one of them is x=0 which is its own negation.

Given zero x=6 we know x=-6 is also a zero.

So we know three zeros, and know the other two zeros are a positive and negative pair.

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

Choice A