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 first step in identifying discontinuities in a rational function?

• Setting the numerator equal to zero

• Finding the domain

• Multiplying the numerator and denominator

• Factoring the denominator

Which of the following is a factor of the quadratic expression x^2 - 4?

• x + 2

• x - 2

• x - 4

• x + 4

What is a removable discontinuity also known as?

• A hole

• A vertical asymptote

• A zero

• An intercept

What happens to the term x + 2 in the simplification process?

• It is multiplied by the numerator

• It becomes a vertical asymptote

• It remains unchanged

• It is removed as a removable discontinuity

Which type of discontinuity is associated with a vertical asymptote?

• Removable

• Oblique

• Non-removable

• Horizontal