Answer
(a) on the curve.
(b) on the curve.
(c) not on the curve.
Work Step by Step
Test each point on $f(x)=x^3-3x+1$, we have:
(a) $f(-2)=(-2)^3-3(-2)+1=-1$, thus it is on the curve.
(b) $f(2)=(2)^3-3(2)+1=3$, thus it is on the curve.
(c) $f(3)=(3)^3-3(3)+1=19\ne 1$, thus it is not on the curve.
