Algebra-2

A. Analyze the option "There is a local max at x = - 5":

The function is increasing before x=-5 and then starts to decrease at x = - 5. By the definition of a local maximum, when a function changes from increasing to decreasing at a point, that point is a local maximum. So, there is a local maximum at x = - 5. This option is correct.

B. Analyze the option "The graph has two absolute minimum":

An absolute minimum is the lowest value of the function over its entire domain. In general, a function has at most one absolute minimum (assuming it is a well - defined function). There is no indication in the given description that there are two such lowest points for the entire graph. So, this option is incorrect.

C. Analyze the option "The graph has five relative extrema":

A relative extremum occurs when the function...