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: 61

Answer

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

Work Step by Step

Solve for $y$ in terms of $x$ to obtain: $\begin{array}{ccc} &2x-4y^2 &= &3 \\&-4y^2 &= &3-2x \\&\dfrac{-4y^2}{-4} &= &\dfrac{3-2x}{-4} \\&y^2 &= &-\dfrac{3}{4}+\dfrac{1}{2}x \\&y &= &\pm \sqrt{-\dfrac{3}{4}+\dfrac{1}{2}x} \end{array}$ 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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