Answer
The equation is symmetric about the origin.
Work Step by Step
$x^{3}-y^{5}=0$
Check for symmetry about the $y$-axis by substituting $x$ by $-x$ in the given equation and simplifying:
$(-x)^{3}-y^{5}=0$
$-x^{3}-y^{5}=0$
Since substituting $x$ by $-x$ in the equation didn't yield an equivalent equation, it is not symmetric about the $y$-axis.
Check for symmetry about the $x$-axis by substituting $y$ by $-y$ in the given equation and simplifying:
$x^{3}-(-y)^{5}=0$
$x^{3}+y^{5}=0$
Since substituting $y$ by $-y$ in the equation didn't yield an equivalent equation, it is not symmetric about the $x$-axis.
Check for symmetry about the origin by substituting $x$ by $-x$ and $y$ by $-y$ in the given equation and simplifying:
$(-x)^{3}-(-y)^{5}=0$
$-x^{3}+y^{5}=0$
Take out common factor $-1$ from the left side:
$(-1)(x^{3}-y^{5})=0$
Take $-1$ to divide the right side:
$x^{3}-y^{5}=\dfrac{0}{-1}$
$x^{3}-y^{5}=0$
Since the substitutions yielded an equivalent equation, it is symmetric about the origin.
The graph is shown in the answer section
