Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 1: Functions - Section 1.1 - Functions and Their Graphs - Exercises 1.1 - Page 13: 69

Answer

We use the graph below as an example of demonstration. The curve is symmetric around the x-axis and is not $ y=0$. If we draw a vertical line, there will be two points on the curve with coordinates $ P_{1}(x,y_{1})$ and $ P_{2}(x,-y_{1})$. We see that unless $ y_{1}=0$, the curve can not be a graph of a function (which requires a single intersection on the graph for each x-value).

Work Step by Step

Given above.
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