Graph a rational function with vertical and oblique asymptotes

The video tutorial covers the process of graphing rational functions with a focus on identifying and graphing vertical, horizontal, and slant asymptotes. It begins with an introduction to vertical asymptotes, followed by a discussion on horizontal and slant asymptotes. The instructor demonstrates how to use long division to find slant asymptotes and graph them. The tutorial also includes finding X and Y intercepts and discusses the behavior of the graph concerning multiplicity of roots. The session concludes with final graphing steps and a summary of the key points.

What is the first step in finding the vertical asymptote?

Explain the significance of the degrees of the polynomials in determining horizontal asymptotes.

What is the process to determine if a slant asymptote exists?

What is the role of synthetic division in finding slant asymptotes?

Describe how to perform long division to find a slant asymptote.

How do you graph a slant asymptote once it is determined?

What are the steps to find the X-intercept of a function?

How do you determine the Y-intercept of a function?

What does it mean for a graph to approach an asymptote?

How does the multiplicity of a zero affect the graph at that point?