Question

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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)?
O (-6, 0), (-2, 0), and (0, 0)
O (-6, 0), (-2, 0), and (4, 0)
O (-4, 0), (0, 0), and (2, 0)
O (-4, 0), (-2, 0), and (0, 0)

Answer 1

The given function is even, which means it is symmetric about the y-axis. Since it has five x-intercepts, and one of them is at (6, 0), the other x-intercepts need to be symmetric to this point across the y-axis. Here's how you can determine the other x-intercepts: 1. Start with the x-intercept given: (6, 0). 2. Find its symmetric point across the y-axis. For a point (a, b), its symmetric point across the y-axis is (-a, b). 3. So, the symmetric point of (6, 0) across the y-axis is (-6, 0). 4. Repeat this process for each x-intercept given in the answer choices. 5. Compare the symmetric points obtained to the other x-intercepts given in the answer choices. After following these steps, you will find that the set of points that can be the other x-intercepts of the graph of f(x) is: O (-6, 0), (-2, 0), and (4, 0). These points are symmetrically positioned across the y-axis relative to the x-intercept at (6, 0), fitting the description of an even function with five x-intercepts.