Graphing a rational functions with asymptotes

The video tutorial covers the concept of slant asymptotes, starting with an introduction to the problem of finding asymptotes for a given function. It explains how to determine vertical asymptotes by setting the denominator to zero and emphasizes the importance of considering both positive and negative solutions. The tutorial then discusses horizontal asymptotes and introduces slant asymptotes, explaining that they occur when the degree of the numerator is greater than the degree of the denominator. The instructor demonstrates how to use long division to find slant asymptotes and concludes with a graphing exercise to visualize the function's behavior.

Why is the remainder not considered when finding the slant asymptote?

What is the equation of the slant asymptote derived from the function?

What is the behavior of the graph as it approaches the asymptotes?

How do you determine the values to plot for the graph?