Label and identify discontinuities of a rational function

The video tutorial explains how to identify and classify discontinuities in rational functions. It begins by introducing the concept of rational functions and the importance of finding discontinuities. The teacher demonstrates how to factor quadratics in both the numerator and denominator to simplify the expression. The process of identifying discontinuities in factored form is discussed, highlighting the ease of finding them. The tutorial further explains the difference between removable discontinuities (holes) and non-removable discontinuities (vertical asymptotes), emphasizing the simplification process and classification of these discontinuities.

What is the relationship between the factors of the numerator and the discontinuities of the function?

Explain the significance of vertical asymptotes in the context of rational functions.