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) = x³ + 4x² - 11x - 30

ƒ(x) = (x - 3)(x + 2)(x + 5)

(a) ƒ(x) = 0 

(b) ƒ(x) 6 0

(c) ƒ(x) 7 0