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9.2 Graphing Simple Rational Functions (Day 1)

Learn about hyperbolas and how to graph rational functions of the form p(x)/q(x), with detailed examples and explanations of vertical and horizontal asymptotes. Understand domain and range concepts for effective graphing.

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9.2 Graphing Simple Rational Functions (Day 1)

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  1. 9.2 Graphing Simple Rational Functions (Day 1) A Rational Function is a function of the form: where p(x) and q(x) are polynomials and q(x) ≠ 0

  2. 9.2 Graphing Simple Rational Functions (Day 1) Rational functions are called HYPERBOLAS. There are 2 types of rational functions. TYPE 1 • a = Decides which quadrants the hyperbola is drawn in • If a > 0, then graph is in quadrants 1 and 3 • If a < 0, then graph is in quadrants 2 and 4 • h = Vertical Asymptote (VA) x = h (Set the denominator = 0, and solve for x) • k = Horizontal Asymptote (HA) y = k • Make a table with 2 x – values on each side of the VA • Domain: All real numbers, except x = h • Range: All real numbers, except y = k

  3. 9.2 Graphing Simple Rational Functions (Day 1) Ex. 1 Give all of the details for the hyperbola and then graph it. x – intercept: set y = 0 and solve for x. Since a > 0, then graph is in quadrants 1 and 3 VA: x = 3 HA: y = 1 Domain: All real numbers, except x = 3 Range: All real numbers, except y = 1

  4. 9.2 Graphing Simple Rational Functions (Day 1)

  5. 9.2 Graphing Simple Rational Functions (Day 1) Ex. 2 Give all of the details for the hyperbola and then graph it. Since a < 0, then graph is in quadrants 2 and 4 VA: x = - 3 HA: y = - 1 Domain: All real numbers, except x = - 3 Range: All real numbers, except y = - 1

  6. 9.2 Graphing Simple Rational Functions (Day 1)

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