Learn How to Find Vertical, Horizontal and Slant Asymptotes of a Rational Function

The video tutorial covers the process of analyzing rational functions by factoring the denominator, identifying vertical and horizontal asymptotes, and determining slant asymptotes using long division. It explains that a vertical asymptote is found by setting the denominator to zero, while horizontal asymptotes depend on the degree of the numerator and denominator. If the numerator's degree is higher, there is no horizontal asymptote, and a slant asymptote is found using long division.

What is the first step in identifying a vertical asymptote of a rational function?

• Compare the degrees of numerator and denominator

• Set the denominator equal to zero

• Factor the numerator

• Set the numerator equal to zero

How do you determine if a rational function has a horizontal asymptote?

• By factoring the numerator

• By comparing the degrees of the numerator and denominator

• By setting the numerator equal to zero

• By using long division

What conclusion can be drawn if the degree of the numerator is greater than the degree of the denominator?

• The function is undefined

• There is a horizontal asymptote

• The degrees must be equal

• There is no horizontal asymptote

Which method is used to find the slant asymptote of a rational function?

• Factoring

• Setting the denominator to zero

• Long division

• Comparing coefficients

What is the equation of the slant asymptote found using long division in the video?

• y = x - 1

• y = 2x

• y = x + 2

• y = x