Question

The table below shows several points from an absolute value function, y = f(x). Which of the following best describes the values of x when f(x) = 4? X -2 -1 0 1 2 3 4 y 5 4 3 2 3 4 5​

Answer 1

The values of x for which f(x) equals 4 in the given table of an absolute value function are -1 and 3, as the nature of such functions presents symmetrical pairs of x-values for a given y-value due to their V-shaped graphs.

Step-by-step explanation:

The student's question relates to an absolute value function and specifically asks which values of x will result in f(x) being equal to 4. From the given points in the table, we can observe that there are two x-values for which f(x) equals 4: -1 and 3. This is indicative of the V-shaped graph that is typical for absolute value functions, which have a central vertex where the graph changes direction.

As the y value increases away from the vertex, the x values come in symmetrical pairs that yield the same y value. Therefore, in the context of the given table and the nature of absolute value functions, the best description for the values of x when f(x) = 4 is x = -1 and x = 3.