Answer
$(0,0) $,
symmetric with respect to the origin.
Work Step by Step
Step 1. For x-intercept(s), let $y=0$, we have $x=0\longrightarrow (0,0)$, for y-intercept(s), let $x=0$, we have $y=0 \longrightarrow (0,0) $,
Step 2. To test for x-axis symmetry, replace $(x,y)$ with $(x,-y)$, we have $-y=\frac{-(x)^3}{(x)^2-9}$ which is different from the original equation, thus it is not symmetric with respect to the x-axis,
Step 3. To test for y-axis symmetry, replace $(x,y)$ with $(-x,y)$, we have $y=\frac{-(-x)^3}{(-x)^2-9}$ which is different from the original equation, thus it is not symmetric with respect to the y-axis,
Step 4. To test for origin symmetry, replace $(x,y)$ with $(-x,-y)$, we have $-y=\frac{-(-x)^3}{(-x)^2-9}$ which is the same as the original equation, thus it is symmetric with respect to the origin.
