Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.3 - Analyzing Graphs of Functions - 2.3 Exercises - Page 197: 97c

Answer

The graph passes through the origin. The graph is symmetric with respect to the origin.

Work Step by Step

We are given the function: $y=x^3$ Graph the function. The graph passes through the origin. The graph is symmetric with respect to the origin. Comparison of the given graphs: - all graphs pass through the origin - the graphs of even power ($y=x^2,y=x^4,y=x^6$) are symmetric with respect to the $y$-axis, while the graphs of odd power ($y=x,y=x^3,y=x^5$) are symmetric with respect to the origin. - as the power increases, the graphs become steeper
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