College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Section 5.1 - Polynomial Functions and Models - 5.1 Assess Your Understanding - Page 339: 69

Answer

The graph meets the requirements to be a polynomial function. Its zeros are (-1,0), (1,0), and (2,0). The least degree it can have is 3.

Work Step by Step

The graph has no points of discontinuity like holes or jumps, nor does it have cusps, so it could be a polynomial function. The real zeros are the same as the x-intercepts which can be seen on the graph. The least degree can be found by adding 1 to the number of turning points (where the graph changes from positive to negative slope or vice-versa). In this case, we can see that there are two turning points; therefore, the least degree this polynomial can have is 3.
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