Master How to determine the horizontal asymptotes of a rational function

The video tutorial explains how to determine horizontal asymptotes of rational functions. It begins with a brief overview of vertical asymptotes and then delves into the horizontal asymptote test. The test involves comparing the degrees of the numerator and denominator polynomials. If the numerator's degree is greater, there is no horizontal asymptote. If it's less, the asymptote is y=0. If the degrees are equal, the asymptote is y=a/b, where a and b are the leading coefficients. The tutorial includes examples and emphasizes the importance of writing polynomials in descending order.

What is the condition for a vertical asymptote in a rational function?

• When the degrees of numerator and denominator are equal

• When the numerator is zero

• When the denominator is zero

• When both numerator and denominator are zero

What happens when the degree of the numerator is greater than the degree of the denominator in a rational function?

• There is no horizontal asymptote

• The horizontal asymptote is y = 0

• The horizontal asymptote is y = a/b

• The function has a vertical asymptote

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

• By setting the numerator to zero

• By setting the denominator to zero

• By the ratio of the leading coefficients

• By subtracting the degrees

In the example where the degree of the numerator is 1 and the degree of the denominator is 2, what is the horizontal asymptote?

• No horizontal asymptote

• y = 0

• y = 2

• y = 1

Why is it important to write polynomials in descending order when determining the degree and leading coefficients?

• To simplify the calculation

• To ensure the correct degree is identified

• To eliminate vertical asymptotes

• To make the function continuous