Question

Use the key features of the polynomial f(x) = -2x3 + 5x2 - 2x - 3 to describe its end behavior.
The left side continues down, and the right side continues up.
The left side continues down, and the right side continues down.
O The left side continues up, and right side continues up.
The left side continues up, and the right side continues down.

Answer 1

Answer:

Step-by-step explanation:

First consider the parent function y = x^3 and its graph.  The left side starts in Quadrant III and continues up through Quadrant I.  A negative sign in front of the x^3 reflects this original graph in the x-axis; the graph now starts in Quadrant II and descends into Quadrant IV.

The end behavior of the given function is the same as that of the graph of y = -x^3;  

The graph begins in Quadrant II and descends into Quadrant IV, down.

Answer 2

      Option (4). The left side continues up and the right side continues down.

End behavior of a polynomial function:

•   If a polynomial function has the odd degree and the leading

           coefficient negative,

           Left end of the graph will continue up and right end will move down.

Given in the question,

Polynomial function → f(x) = -2x³ + 5x² - 2x - 3

Leading coefficient = (-2)

Degree of the polynomial = 3

Since, degree of the polynomial given is odd and the leading coefficient is negative,

     Therefore, left side of the graph will continue up and the right side continues down.

                      Option (4) will be the answer.

Learn more about the end behavior of a polynomial function here,

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