Answer
Only the following points are on the graph of the given equation:
(a) $(-2, -1)$
(b) $(2, 3)$
Work Step by Step
A point is on the graph of a given equation if its x and y coordinates satisfy the equation.
Substitute the coordinates of each point into the given equation to obtain:
(a)
$y=x^3-3x+1
\\-1 = (-2)^3-3(-2) + 1
\\-1 = -8 + 6 + 1
\\-1 = -2+1
\\-1=-1$
(b)
$y=x^3-3x+1
\\3=2^3-3(2)+1
\\3 = 8-6+1
\\3=2+1
\\3=3$
(c)
$y=x^3-3x+1
\\1=3^3-3(3)+1
\\1=27-9+1
\\1=18+1
\\1\ne19$
Thus, only the points in (a) and in (b) are on the graph of the given equation.
