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Exploring Simple Rational Functions Graphing

Learn to graph simple rational functions, understand vertical and horizontal asymptotes, and interpret the branches of hyperbolas. Practice with examples and solve for domain and range. Try solving assignments for better understanding.

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Exploring Simple Rational Functions Graphing

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  1. 9.2 Graphing Simple Rational Functions (p. 540)

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

  3. Hyperbola 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

  4. Hyperbola (continued) • One form: • Has 2 asymptotes: x=h (vert.) and y=k (horiz.) • Graph 2 points on either side of the vertical asymptote. • Draw the branches.

  5. 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.

  6. Ex: Graph State the domain & range. Vertical Asymptote: x=1 Horizontal Asymptote: y=2 x y -5 1.5 -2 1 0 -1 4 3 Left of vert. asymp. Right of vert. asymp. Domain: all real #’s except 1. Range: all real #’s except 2.

  7. Ex: GraphState 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.

  8. You try! 

  9. You try! 

  10. Assignment543-544/12-39 mult. of 3

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