Limits at infinity

The video tutorial discusses the identification and understanding of asymptotes in polynomial and rational functions. It covers horizontal asymptotes when the degree of the numerator is less than or equal to the denominator, and introduces slant or oblique asymptotes when the numerator's degree is greater. The tutorial emphasizes the importance of recognizing these asymptotes to understand the end behavior of graphs.

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

• y = 0

• y = x

• y = 1

• y = infinity

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

• By the product of the coefficients

• By the difference of the coefficients

• By the sum of the coefficients

• By the ratio of the leading coefficients

What happens to the graph of a rational function as it approaches its horizontal asymptote?

• It remains constant

• It oscillates around the asymptote

• It diverges away from the asymptote

• It approaches the asymptote

What type of asymptote is present when the degree of the numerator is greater than the degree of the denominator?

• No asymptote

• Horizontal asymptote

• Vertical asymptote

• Slant or oblique asymptote

Which method can be used to quickly determine the behavior of a graph with a slant asymptote?

• Using the leading coefficient terms

• Using the degree of the denominator

• Using the sum of all coefficients

• Using the constant term