How to graph a rational function by simplifying to the reciprocal functions

The video tutorial covers the concepts of horizontal and vertical asymptotes, explaining how to determine them by comparing polynomial degrees and coefficients. It also discusses finding X and Y intercepts, emphasizing the importance of setting the numerator to zero for X intercepts. The tutorial further explores the domain and range of functions, suggesting graphing as a method to verify range. Finally, it introduces long division and mixed numbers, demonstrating how to represent rational functions in different forms.

What is the process to determine the horizontal asymptote of a rational function?

Explain how to find the vertical asymptote of a rational function.

What is the significance of the X and Y intercepts in graphing a rational function?

How do you determine the domain of a rational function?

Describe the method to find the range of a rational function.

How can long division be applied to rational functions, and what is its purpose?

What is the relationship between improper fractions and mixed numbers in the context of rational functions?