Learn how to find the asymptotes of a rational function

The video tutorial covers the identification of vertical and horizontal asymptotes in rational functions. It begins with an introduction to asymptotes and the homework task of finding them. The teacher explains rational functions, emphasizing the importance of polynomials in both the numerator and denominator. The process of finding vertical asymptotes is demonstrated using the zero product property. The tutorial concludes with a discussion on horizontal asymptotes, focusing on the relationship between the degrees of the numerator and denominator polynomials.

What is the first step in analyzing a rational function for asymptotes?

• Set the numerator equal to zero

• Ensure the polynomials are fully expanded

• Find the roots of the numerator

• Identify the leading coefficients

How do you determine the vertical asymptotes of a rational function?

• By comparing the degrees of the numerator and denominator

• By finding the leading coefficient of the numerator

• By setting the denominator equal to zero

• By setting the numerator equal to zero

What is the vertical asymptote for the function given in the video?

• x = 0 and x = 4

• x = 1 and x = -1

• x = 3 and x = -3

• x = 2 and x = -2

What determines the horizontal asymptote when the degree of the numerator is less than the degree of the denominator?

• y = 1

• y = 0

• No horizontal asymptote

• y = the leading coefficient of the numerator

If the degrees of the numerator and denominator are equal, how is the horizontal asymptote determined?

• y = 0

• y = the leading coefficient of the denominator

• No horizontal asymptote

• y = the ratio of the leading coefficients