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 4x 2 11x 30 (x) (x 3)(x 2)(x 5) (a) (x) 0 (b) (x) 6 0 (c) (x) 7 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 + 4x² - 11x - 30

ƒ(x) = (x - 3)(x + 2)(x + 5)

(a) ƒ(x) = 0

(b) ƒ(x) 6 0

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