the graph of the even function f(x) has five x - intercepts. if (6, 0) is one of the intercepts, which set…

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)

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

Explanation:

Step1: Recall property of even functions

An even function satisfies $f(x)=f( - x)$. So if $(a,0)$ is an $x$-intercept (i.e., $f(a) = 0$), then $f(-a)=0$ and $(-a,0)$ is also an $x$-intercept. Since $(6,0)$ is an $x$-intercept, then $(-6,0)$ must be an $x$-intercept. Among the given options, only the first option contains $(-6,0)$.

Answer:

A. $(-6,0),(-2,0)$, and $(0,0)$