Page 4: Advanced Examples and Applications

This page provides multiple complex examples demonstrating the complete process of analyzing and graphing rational functions.

Example: The function f(x) = (5x-10)/(x²+x-6) is analyzed showing a hole at (2,1), vertical asymptote at x = -3, and horizontal asymptote at y = 0.

Highlight: Each example demonstrates different combinations of features including holes, asymptotes, and intercepts.

Vocabulary: DNE (Does Not Exist) is used to indicate when certain features are not present in a rational function.

Page 1: Introduction to Rational Functions and Asymptotes

This page introduces the fundamental concepts of rational functions and their key components. A rational function is explained as a ratio of two polynomials, with emphasis on branches and asymptotes.

Definition: A rational function is expressed as f(x)/g(x) where f(x) and g(x) are polynomials.

Highlight: A rational function has one more branch than the number of vertical asymptotes.

Example: The function y = (x-3)/(x²-9) demonstrates vertical asymptotes at x = -3 and x = 3.

Vocabulary: Branches refer to the continuous portions of a rational function graph separated by vertical asymptotes.