Ch. 11 Vocabulary 7.) Rational function 8.) Asymptote.

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Ch. 11 Vocabulary 7.) Rational function 8.) Asymptote

11-7 Graphing Rational Functions Algebra I

Rational Function A function of the form where p(x) & q(x) are polynomials and q(x)≠0.

Hyperbola A type of rational function. x=0 A type of rational function. Has 1 vertical asymptote and 1 horizontal asymptote. Has 2 parts called branches. (blue parts) They are symmetrical. We’ll discuss 2 different forms. y=0

Hyperbola (continued)

Ex 1: Graph Identify the asymptotes.

Ex 2: Graph Identify the asymptotes.

Ex 3: Graph Identify the asymptotes.

Ex. Ex.4 Describe the graph of each function.

Assignment

Hyperbola (continued) Second form: Vertical asymptote: Set the denominator equal to 0 and solve for x. Horizontal asymptote: Graph 2 points on either side of the vertical asymptote. Draw the 2 branches.

Ex 2: Graph State domain & range.

Assignment

Ex 1: Graph State the domain & range. Vertical Asymptote: x=1 Horizontal Asymptote: y=2 x y -5 1.5 -2 1 2 5 4 3 Left of vert. asymp. Right of vert. asymp. Domain: all real #’s except 1. Range: all real #’s except 2.

Ex 2: Graph State domain & range. Vertical asymptote: 3x+3=0 (set denominator =0) 3x=-3 x= -1 Horizontal Asymptote: x y -3 .83 -2 1.33 0 -.67 2 0 Domain: All real #’s except -1. Range: All real #’s except 1/3.