## College Algebra (10th Edition)

Only the following points are on the graph of the given equation: (a) $(-2, -1)$ (b) $(2, 3)$
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.