Learning to write the domain of a rational function with an asymptotes and hole

The video tutorial explains how to identify discontinuities in functions by examining where the denominator equals zero. It distinguishes between holes and asymptotes, explaining that holes can be factored out while asymptotes cannot. The process involves factoring both the numerator and denominator to determine the type of discontinuity. The tutorial concludes by defining the domain of the function, excluding the points of discontinuity.

What is the significance of setting the denominator equal to zero?

Describe the process of factoring the numerator and denominator as mentioned in the text.