select the correct answer. which statement best describes the graphed function? a. the function has a…

select the correct answer. which statement best describes the graphed function? a. the function has a relative maximum at (-2,4) and a relative minimum at (2,-4). b. the function has a relative minimum at (-2,4) and a relative maximum at (2,-4). c. the function has an absolute maximum at (-2,4) and an absolute minimum at (2,-4). d. the function has an absolute minimum at (-2,4) and an absolute maximum at (2,-4).

select the correct answer. which statement best describes the graphed function? a. the function has a relative maximum at (-2,4) and a relative minimum at (2,-4). b. the function has a relative minimum at (-2,4) and a relative maximum at (2,-4). c. the function has an absolute maximum at (-2,4) and an absolute minimum at (2,-4). d. the function has an absolute minimum at (-2,4) and an absolute maximum at (2,-4).

Answer

Answer:

A. The function has a relative maximum at (-2,4) and a relative minimum at (2,-4).

Explanation:

Step1: Identify relative extrema

Relative maximum is a point where function changes from increasing to decreasing. Relative minimum is a point where function changes from decreasing to increasing.

Step2: Analyze the graph

From the graph, at x = - 2, y = 4 is a peak (function changes from increasing to decreasing), so (-2,4) is a relative - maximum. At x = 2, y=-4 is a trough (function changes from decreasing to increasing), so (2,-4) is a relative - minimum.

Step3: Check for absolute extrema

The graph extends infinitely up and down in both directions, so there are no absolute maximum or minimum. Thus, option A is correct.