Determine whether the graph could be the graph of a polynomial function.

Question

Determine whether the graph could be the graph of a polynomial function. If it could​ be, list the real zeros and state the least degree the polynomial can have.

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A coordinate system has a horizontal x-axis labeled from negative 5 to 5 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. From left to right, a curve rises at a decreasing rate in quadrant 3, crossing the x-axis at x = negative 1 comma and crossing the y dash axis at approximately y equals 3.2 to a maximum in quadrant 1 comma falls and crosses the x dash axis at x equals 3 to a minimum in quadrant 4 comma and rises at an increasing rate comma crossing the x dash axis at x equals 5.

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Part 1

Select the correct choice below and fill in any answer boxes within your choice.

A.

The graph shows a polynomial function. The real​ zero(s) is/are

enter your response here.

The least degree the polynomial can have is

enter your response here.

​(Use a comma to separate answers as needed. Round to the nearest integer as​ needed.)

B.

The graph does not show a polynomial function.

Answer 1

The graph crooses the x-axis at -1, 3, and 5, so those are real zeros and there are at least 3 factors, namely x-3, x-5, and x+1. So, the polynomial would have degree 3 or larger.