Answer
(a) $(0,0),(\pm2,0)$, (b) symmetric with respect to the origin. (c) See graph.
Work Step by Step
(a) Given $y=x^3-4x$, we can find the x-intercept(s) (let y=0) as $(0,0),(\pm2,0)$, y-intercept(s) (let x=0) as $(0,0)$,
(b) To test symmetry, replace $(x,y)$ with $(x,-y)$ (x-axis symmetry), or $(-x,y)$ (y-axis symmetry), or $(-x,-y)$ (origin symmetry), and we can find the equation is symmetric with respect to the origin.
(c) See graph.
