Answer
(a) The graph is symmetric about the $x$-axis, the $y$-axis and the origin.
(b) $y = (1 − x^\frac{2}{3})^\frac{3}{2}.$
(c) For quadrant $II$, the same; for $III$ and $IV$ use $y = −(1 − x^\frac{2}{3})^\frac{3}{2}$
Work Step by Step
(a) Whether we replace $x$ with $−x$, $y$ with $−y$, or both, we obtain the same equation, so by Theorem 0.2.3 the graph is symmetric about the $x$-axis, the $y$-axis and the origin.
