Question

Below is the graph of a polynomial function with real coefficients. All local extrema 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.
(b) At which x-values does the function have local maxima? If there is more than one
value, separate them with commas.
(c) What is the sign of the function's leading coefficient?
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(d) Which of the following is a possibility for the degree of the function? Choose all that
apply.

Answer 1

The decreasing intervals are (-9, -5), (-1, 5) and (9, ∝)

The local maxima are x = -9, x = -1 and x = 9

The sign of the function's leading coefficient is negative

The possible degree of the function is 6

How to determine the decreasing intervals

From the question, we have the following parameters that can be used in our computation:

The graph

From the graph, we have the following

Decreasing interval = (-9, -5), (-1, 5) and (9, ∝)

This is because the y values decrease as x increase

At which x-values does the function have local maxima?

By definition,

The local maxima is where the function's value is greater than all of the values of the function surrounding it

Using the above as a guide, we have the following local maxima

x = -9, x = -1 and x = 9

The sign of the function's leading coefficient

From the graph, we can see that the graph opens down

A graph that opens down has a negative leading coefficient

Hence, the sign of the function's leading coefficient is negative

The degree of the function

From the figure, we can see that

The graph has 6 turning points

This means that the possible degree of the function is 6