Finding the Slant Asymptote

The video tutorial explains how to find vertical, horizontal, and slant asymptotes in rational functions. It begins with identifying vertical asymptotes by setting the denominator equal to zero. Then, it covers horizontal asymptotes, determined by comparing the degrees of the numerator and denominator polynomials. If the numerator's degree is higher, a slant asymptote is present, which is found using long division. The tutorial emphasizes understanding graph behavior near these asymptotes.

What are vertical asymptotes and how do you find them?

Illustrate how to sketch a graph showing vertical and horizontal asymptotes.

Explain the process of finding horizontal asymptotes.

What is the significance of the degrees of the leading terms in determining horizontal asymptotes?

Describe the conditions under which a rational function does not have a horizontal asymptote.

How do you find slant asymptotes and why is long division used?

What is the role of synthetic division in finding asymptotes?