For any function y (x), the following hold true (a) The real solutions of (x) 0 correspond to the x intercepts of the graph (b) The real solutions of (x) 0 are the x values for which the graph lies below the x axis (c) The real solutions of (x) 0 are the x values for which the graph lies above the x axis In each exercise, a polynomial function (x) is given in both expanded and factored forms Graph each function, and solve the equations and inequalities Give multiplicities of solutions when applicable (x) x 3 3x 2 6x 8 (x) (x 4)(x 1)(x 2) (a) (x) 0 (b) (x) 0 (c) (x) 0

Question: For any function y = (x), the following hold true. (a) The real solutions of (x) = 0 correspond to the x-intercepts of the graph.

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.

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 - 3x² - 6x + 8

ƒ(x) = (x - 4)(x - 1)(x + 2)

(a) ƒ(x) = 0

(b) ƒ(x) < 0

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