what is the correct answerThe 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)

Question

what is the correct answer>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)

anonymous · Answer

Even functions are symmetric about the y-axis, so if (6, 0) is an intercept, then (-6,0) is also an intercept. All your choices have (0,0), so you the other two intercepts have to be opposites. Meaning you can have either ±2 or ±4, but not a mix of both.