Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.1 Review of Functions - 1.1 Exercises: 75

Answer

The equation is symmetric about the $x$-axis, the $y$-axis and the origin.
1512704523

Work Step by Step

$x^{2/3}+y^{2/3}=1$ Check for symmetry about the $y$-axis by substituting $x$ by $-x$ in the given expression and simplifying: $(-x)^{2/3}+y^{2/3}=1$ $\sqrt[3]{(-x)^{2}}+y^{2/3}=1$ $\sqrt[3]{x^{2}}+y^{2/3}=1$ $x^{2/3}+y^{2/3}=1$ Since substituting $x$ by $-x$ yielded an equivalent expression, the equation is symmetric about the $y$-axis Check for symmetry about the $x$-axis by substituting $y$ by $-y$ in the given expression and simplifying: $x^{2/3}+(-y)^{2/3}=1$ $x^{2/3}+\sqrt[3]{(-y)^{2}}=1$ $x^{2/3}+\sqrt[3]{y^{2}}=1$ $x^{2/3}+y^{2/3}=1$ Since substituting $y$ by $-y$ yielded an equivalent expression, the equation is symmetric about the $x$-axis Since the equation is symmetric to both the $x$ and $y$-axis, it is also symmetric about the origin. The graph is shown in the answer section.
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.