Question

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

Below is the graph of a polynomial function with real comedic fangs. All local extreme of the function are shown in the graph.
Use the graph to answer the following questions.

(a) over which intervals is the function decreasing? Choose all that apply.
(-∞,-8) (-8,-4) (-4,0) (0,5) (-4,5) (9, ∞)

(b) At which x-values does the function have local minima? If there is more than one value seepage them with commas.

(C) what is the sign of the function’s leading coefficient?
Answers are positive, negative, not enough time

(D) which of the following is a possibility for the degree of the function? Choose all that apply
4 , 5 , 6 , 7 , 8 , 9

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