Question

PLEASE HELP I WILL GIVE BRAINLEST!!!!!!

Answer 1

Part (a)

Decreasing means that as x increases, y decreases.

So the intervals are $(-8, -4), (0, 5), (9, \infty)$

Part (b)

A local minimum is where the function changes from decreasing to increasing.

So, the local minima are at $x=-4, 5$

Part (c)

The function is approaching negative infinity as x approaches both positive and negative infinity, so the leading coefficient is negative

Part (d)

The degree is given by the number of roots (including multiplicity).

From the graph, we see there is a single root at x = -6, a single root at x = -1, a single root at x = 1, a single root between x=6 and x=8, and a single root at around x = 10.

Thus, there are a minimum of 5 roots for the graph (there could be more outside of the given section)

However, since the graph has the same end behavior in both directions, the degree must be even.

So, the possible answers are any even number that is at least 6