Answer
$x=0,\pm3$, $y=0$,
origin symmetry.
Work Step by Step
Step 1. Given $y=x^3-9x$, to find the x-intercept(s), let $y=0$, we have $x(x^2-9)=0$, thus $x=0,\pm3$
Step 2. To find the y-intercept(s), let $x=0$, we have $y=0$ or $(0,0)$
Step 3. To test symmetry, replace $(x,y)$ with $(x,-y)$ (x-axis symmetry), or $(-x,y)$ (y-axis symmetry), or $(-x,-y)$ (origin symmetry), and see if the equation remain unchanged. We can find only an origin symmetry.
