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9.2 Graphing Simple Rational Functions

9.2 Graphing Simple Rational Functions. (p. 540). Rational Function. A function of the form where p(x) & q(x) are polynomials and q(x) ≠0. Hyperbola. x=0. A type of rational function. Has 1 vertical asymptote and 1 horizontal asymptote.

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9.2 Graphing Simple Rational Functions

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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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