Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.3 - More on Functions and Their Graphs - Exercise Set - Page 196: 17

Answer

The graph of the equation $y={{x}^{2}}+6$ is symmetric to the y-axis only.

Work Step by Step

Consider the equation, $y={{x}^{2}}+6$ Check the symmetry about the y-axis: An equation is symmetric about the y-axis if $-x$ is substituted in the function and the result is an equivalent equation. Substitute $x=-x$ in the equation, $\begin{align} & y={{\left( -x \right)}^{2}}+6 \\ & ={{x}^{2}}+6 \end{align}$ Therefore, the equation is symmetric about the y-axis. Now, check symmetry about the x-axis: An equation is symmetric about the x-axis if $-y$ is substituted in the function and it leads to an equivalent equation. Substitute $y=-y$, $-y={{x}^{2}}+6$ Therefore, the equation is not symmetric about the x-axis. Now, check symmetry about the origin: A equation is symmetric about the origin if $x=-x,y=-y$ and it leads to an equivalent equation. Substitute $x=-x,y=-y$ $\begin{align} & -y={{\left( -x \right)}^{2}}+6 \\ & -y={{x}^{2}}+6 \\ \end{align}$ Therefore, the equation is not symmetric about the origin. Hence, the equation is only symmetric about the y-axis.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.