Find the vertical and horizontal asymptotes

The video tutorial explains how to find vertical and horizontal asymptotes of functions. It begins with an introduction to asymptotes, describing them as lines that a graph approaches but never reaches. The tutorial then details the process of finding vertical asymptotes by setting the denominator of a function to zero and solving for x. It also covers horizontal asymptotes, explaining how to compare the degrees of the numerator and denominator to determine the asymptote. The video concludes with examples illustrating these concepts.

What is an asymptote in the context of graph behavior?

• A curve that the graph follows exactly

• A point where the graph intersects the y-axis

• A point where the graph intersects the x-axis

• A line that a graph never crosses

How do you find the vertical asymptotes of a function?

• By finding the derivative of the function

• By setting the denominator to zero

• By setting the function equal to zero

• By setting the numerator to zero

Why might a function not have a vertical asymptote?

• Because the function is linear

• Because the denominator has no real roots

• Because the numerator is zero

• Because the function is quadratic

What determines the horizontal asymptote of a function?

• The roots of the denominator

• The constant term of the function

• The degree of the numerator and denominator

• The coefficients of the numerator

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

• By the sum of the coefficients

• By the difference of the coefficients

• By the ratio of the leading coefficients

• By the product of the coefficients