8 4 Rational Functions A rational function is

8 -4 Rational Functions A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) = x 1. Its graph is a hyperbola, which has two separate branches. Rational functions may have asymptotes (boundary lines). 1 The f(x) = x has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. Holt Algebra 2

8 -4 Rational Functions Notes: Graphing Hyperbolas 1 1 A. Graph g(x) = x +6 1 B. Graph g(x) = - 1 x +6 2 - 4 2. Graph g(x) = x 3. Identify the asymptotes, domain, and range of the function g(x) = 1 – 4. x +6 Holt Algebra 2

8 -4 Rational Functions The rational function f(x) = 1 can be transformed x by using methods similar to those used to transform other types of functions. Holt Algebra 2

8 -4 Rational Functions Example 1: Transforming Rational Functions 1 Using the graph of f(x) = x as a guide, describe the transformation and graph each function. A. g(x) = 1 x+2 translate f 2 units left. Holt Algebra 2 B. g(x) = 1 – 3 x translate f 3 units down.

8 -4 Rational Functions Example 2 1 Using the graph of f(x) = x as a guide, describe the transformation and graph each function. a. g(x) = 1 x+4 translate f 4 units left. Holt Algebra 2 b. g(x) = 1 + 1 x translate f 1 unit up.

8 -4 Rational Functions A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) = x 1. Its graph is a hyperbola, which has two separate branches. Rational functions may have asymptotes (boundary lines). 1 The f(x) = x has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. Holt Algebra 2

8 -4 Rational Functions The values of h and k affect the locations of the asymptotes, the domain, and the range of rational functions whose graphs are hyperbolas. Holt Algebra 2

8 -4 Rational Functions Notes: Graphing Hyperbolas 1 1 A. Graph g(x) =x +6 -1 1 B. Graph g(x) = x +6 2. Graph g(x) = Holt Algebra 2 x 2 - 4

8 -4 Rational Functions Notes: Graphing Hyperbolas 3. Identify the asymptotes, domain, and range 1 of the function g(x) = – 4. x +6 Vertical asymptote: x = – 6 Domain: all reals except x ≠ – 6 Horizontal asymptote: y = – 4 Range: all reals except y ≠ – 4 Holt Algebra 2