Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 1 - Section 1.1 - Four Ways to Represent a Function - 1.1 Exercises - Page 18: 9

Answer

No

Work Step by Step

$x^2+(y-3)^2=5$ In this equation, $y$ is not a function of $x$ because for some input values, there are two possible output values. For example, consider $x=1$. $1^2+(y-3)^2=5$ $(y-3)^2=4$ $y-3=\pm2$, which means $y-3=2$ or $y-3=-2$. Therefore, $y$ can be either $5$ or $1$. See image for graph of function. Notice it does not pass the vertical line test.
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