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)?\n(-6, 0), (-2, 0), and (0, 0)\n(-6, 0), (-2, 0), and (4, 0)\n(-4, 0), (0, 0), and (2, 0)\n(-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)?\n(-6, 0), (-2, 0), and (0, 0)\n(-6, 0), (-2, 0), and (4, 0)\n(-4, 0), (0, 0), and (2, 0)\n(-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 ((-a,0)) is also an (x) - intercept. Since ((6,0)) is an (x) - intercept, ((-6,0)) must be an (x) - intercept.

Step2: Check each option

We need to find an option that contains ((-6,0)).

  • Option 1: ((-6,0),(-2,0)), and ((0,0)) contains ((-6,0)).
  • Option 2: ((-6,0),(-2,0)), and ((4,0)) contains ((-6,0)).
  • Option 3: ((-4,0),(0,0)), and ((2,0)) does not contain ((-6,0)).
  • Option 4: ((-4,0),(-2,0)), and ((0,0)) does not contain ((-6,0)).

Answer:

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