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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)?

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)

Respuesta :

The set of points are (0, 0)(–6, 0)
elevatorP6
There seems to be a flaw with this question because it says that there are five x-intercepts but the given information only gives you 4 x-intercepts to work with.

Even means the graph is symmetric about the y-axis

The best answer is A.(–6, 0), (–2, 0), and (0, 0)

because you do not have to worry about another point (0,0). Plus we need (-6,0) for it to be symmetric with (6,0).

Consider function f(x) = x²(x-6)(x+6)(x+2)²(x-2)². It is even and fits these conditions as it has x-intercepts at (6,0), (-6,0), (-2,0), (2,0), and (0,0). again, the question does not tell us the fifth x-intercept, so we need to assume that there is another one that needs to be there...and so (-2,0) must have (2,0) for it to be even as well.

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