Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.6 - Limits at Infinity; Horizontal Asymptotes - 2.6 Exercises - Page 139: 56

Answer

We can see a sketch of the graphs of the five functions.
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Work Step by Step

(i) $y=x^0 = 1$ This graph is a horizontal line. (ii) $y=x^n~~~$ where $n\gt 0$ and $n$ is an odd integer This is an odd function because $(-x)^n = -x^n$ (iii) $y=x^n~~~$ where $n\gt 0$ and $n$ is an even integer This is an even function because $(-x)^n = x^n$ (iv) $y=x^n~~~$ where $n\lt 0$ and $n$ is an odd integer This is an odd function because $(-x)^n = -x^n$ (v) $y=x^n~~~$ where $n\lt 0$ and $n$ is an even integer This is an even function because $(-x)^n = x^n$ Note that all five graphs intersect at the point $(1,1)$ because $~~1^n = 1~~$ for all real numbers
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