For any function y = (x), the following hold true. (a) The real solutions of (x) =

For any function y = ƒ(x), the following hold true.

(a) The real solutions of ƒ(x) = 0 correspond to the x-intercepts of the graph.

(b) The real solutions of ƒ(x) < 0 are the x-values for which the graph lies below the x-axis.

(c) The real solutions of ƒ(x) > 0 are the x-values for which the graph lies above the x-axis.

In each exercise, a polynomial function ƒ(x) is given in both expanded and factored forms. Graph each function, and solve the equations and inequalities. Give multiplicities of solutions when applicable.

ƒ(x) = -x⁴ - 4x³ + 3x² + 18x

ƒ(x) = x(2 - x)(x + 3)²

(a) ƒ(x) = 0

(b) ƒ(x) ≥ 0

(c) ƒ(x) ≤ 0