Graphing Rational Functions

Graphing rational functions involves plotting equations where two polynomials are divided, creating a curve known as a rational graph. To do this, we find key features such as intercepts, asymptotes, and points where the graph behaves differently. Vertical asymptotes occur at values that make the denominator zero, indicating the graph shoots up or down near these points. Horizontal or oblique asymptotes describe the long-term behavior of the graph as x becomes very large or small. By analyzing these features and calculating specific points, you can sketch an accurate graph that reveals the function's overall shape and key behaviors.