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: 66

Answer

$y$ is NOT a function of $x$

Work Step by Step

Solve for $y$ in terms of $x$ to obtain: $\begin{array}{ccc} &2x+|y| &= &0 \\&2x+|y| - 2x &= &0-2x \\&|y| &= &-2x \end{array}$ RECALL: $|x|=a \longrightarrow x = a \text{ or } x = -a$ Use the definition of absolute value to obtain: $|y| = -2x \longrightarrow y = -2x \text{ or } y = 2x$ This means that for every value of $x$, there corresponds two different values of $y$. Thus, the given equation does not represent $y$ as a function of $x$.
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