College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Section 2.2 - Graphs of Functions - 2.2 Exercises - Page 204: 60


$y$ is NOT a function of $x$.

Work Step by Step

Solve for $y$ in terms of $x$ to obtain: $\begin{array}{ccc} &x^2+(y-1)^2 &= &4 \\&(y-1)^2 &= &4-x^2 \\&\sqrt{(y-1)^2} &= &\pm\sqrt{4-x^2} \\&y-1 &= &\pm\sqrt{4-x^2} \\&y &= &1 \pm\sqrt{4-x^2} \end{array}$ The last equation above will give two different values of $y$ for each value of $x$. Thus, the equation does not represent $y$ as a function of $x$.
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