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)?

Because f is even, its graph is symmetric about the y-axis, so if (6, 0) is an x-intercept, then (−6, 0) must be one too. With five x-intercepts total, the remaining intercepts must include (0, 0) and a matching pair at opposite x-values. Choice A gives (−2, 0), which means (2, 0) is also an intercept; together with (−6, 0), (0, 0), and the given (6, 0), that makes five.

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