Finding the vertical and horizontal asymptotes

The video tutorial explains rational functions, focusing on identifying horizontal and vertical asymptotes. It begins by defining rational functions and their components, such as the numerator and denominator polynomials. The instructor then demonstrates how to apply the horizontal asymptote test by comparing the degrees of the polynomials. The horizontal asymptote is determined to be y=0 when the degree of the numerator is less than that of the denominator. For vertical asymptotes, the video emphasizes the importance of simplifying expressions and using the zero product property to find values that make the denominator zero, which are potential vertical asymptotes.

What is the horizontal asymptote of a rational function when the degree of the numerator is less than the degree of the denominator?

• y = 0

• x = 0

• y = 1

• x = 1

Why is it important to simplify a rational expression before determining vertical asymptotes?

• To find the horizontal asymptote

• To make calculations easier

• To change the degree of the polynomials

• To ensure all values making the denominator zero are asymptotes

What is the first step in finding vertical asymptotes of a rational function?

• Factor the numerator

• Simplify the expression

• Set the numerator equal to zero

• Identify the horizontal asymptote

Which property is used to find the vertical asymptotes after factoring the denominator?

• Associative Property

• Distributive Property

• Zero Product Property

• Commutative Property

What are the vertical asymptotes for the function given in the video?

• x = 3 and x = -3

• x = 4 and x = -4

• x = 2 and x = -4

• x = 2 and x = -2