Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter P - P.1 - Graphs and Models - Exercises: 38

Answer

The graph is symmetric with respect to the $x$-axis, but not with respect to the $y$-axis and origin.

Work Step by Step

$|y| - x = 3$ The graph of an equation in $x$ and $y$ is symmetric with respect to the $y$-axis when replacing $x$ by $-x$ yields an equivalent equation. If $|y| - x = 3$ then $|y| + x \ne 3$ The graph of an equation in $x$ and $y$ is symmetric with respect to the $x$-axis when replacing $y$ by $-y$ yields an equivalent equation. $|y|$ means $-y = y$ so nothing changes to $y$ meaning nothing changes in the equation. The graph of an equation in $x$ and $y$ is symmetric with respect to the origin when replacing $x$ by $-x$ and $y$ by $-y$ yields an equivalent equation. As explained before nothing changes to $y$ but something changes to $x$ so the resulting equation is not equivalent to the original.
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