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?

Evaluate responses using AI:

OFF

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

Evaluate responses using AI:

OFF

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

Evaluate responses using AI:

OFF

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

Evaluate responses using AI:

OFF

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

Evaluate responses using AI:

OFF

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

Evaluate responses using AI:

OFF

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

Evaluate responses using AI:

OFF

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

Evaluate responses using AI:

OFF

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

Evaluate responses using AI:

OFF

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

Evaluate responses using AI:

OFF