Answer
a) yes; b) yes; c) no
Work Step by Step
We are given the function:
$y=x^3-3x+1$
a) Check if the point $(-2,-1)$ is on the graph:
$(-2)^3-3(-2)+1\stackrel{?}{=}-1$
$-8+6+1\stackrel{?}{=}-1$
$-1=-1\checkmark$
The point $(-2,-1)$ is on the graph.
b) Check if the point $(2,3)$ is on the graph:
$2^3-3(2)+1\stackrel{?}{=}3$
$8-6+1\stackrel{?}{=}3$
$3=3\checkmark$
The point $(2,3)$ is on the graph.
c) Check if the point $(3,1)$ is on the graph:
$3^3-3(3)+1\stackrel{?}{=}1$
$27-9+1\stackrel{?}{=}1$
$19\not=1$
The point $(3,1)$ is not on the graph.
