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: 9

Answer

It always contains the following points: $(-1, 1), (0,0), \text{and} (1,1)$.

Work Step by Step

Whenever x equals 0, y will always equal zero no matter what power x is raised to. Thus, $(0,0)$ is always a point on a graph of this function. Whenever x is one, y will be one no matter what n is, so $(1,1)$ is on the graph of $y=x^n$ no matter what. Finally, since we are given that n is even, $(-1, 1)$ will be on the graph, for -1 raised to any even power is equal to one.
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