Download presentation

Presentation is loading. Please wait.

Published byRichard Keene Modified over 2 years ago

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

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

3
Holt Algebra Rational Functions The rational function f(x) = can be transformed by using methods similar to those used to transform other types of functions. 1 x

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

5
Holt Algebra Rational Functions Example 2 a. g(x) = translate f 4 units left. 1 x + 4 b. g(x) = translate f 1 unit up. 1 x + 1 Using the graph of f(x) = as a guide, describe the transformation and graph each function. 1 x

6
Holt Algebra Rational Functions Rational functions may have asymptotes (boundary lines). The f(x) = has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0. 1 x A rational function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x) =.Its graph is a hyperbola, which has two separate branches. 1 x

7
Holt Algebra 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.

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

9
Holt Algebra Rational Functions 3. Identify the asymptotes, domain, and range of the function g(x) = – 4. Notes: Graphing Hyperbolas Vertical asymptote: x = –6 Domain: all reals except x –6 Horizontal asymptote: y = –4 1 x +6 Range: all reals except y –4

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google