Learn How to Determine Slant Asymptote of a Rational Function

The video tutorial covers the identification and calculation of vertical, horizontal, and slant asymptotes in rational functions. It begins with vertical asymptotes, explaining the process of setting the denominator to zero and checking for factorability. The tutorial then moves to horizontal asymptotes, focusing on comparing the degrees of the numerator and denominator. Finally, it discusses slant asymptotes, demonstrating the use of long division to find them when the degree of the numerator is greater than the denominator.

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

• Factor the denominator

• Set the numerator equal to zero

• Factor the numerator

• Set the denominator equal to zero

When does a horizontal asymptote occur at y = 0?

• When the leading coefficients are equal

• When the degrees of the numerator and denominator are equal

• When the degree of the numerator is less than the degree of the denominator

• When the degree of the numerator is greater than the degree of the denominator

What is the condition for a slant asymptote to exist?

• The degree of the numerator is less than the degree of the denominator

• The leading coefficients are equal

• The degree of the numerator is equal to the degree of the denominator

• The degree of the numerator is greater than the degree of the denominator

In the process of finding a slant asymptote, what is the role of the remainder?

• It determines the slant asymptote

• It is added to the quotient

• It is ignored

• It is subtracted from the quotient

What mathematical operation is primarily used to find a slant asymptote?

• Synthetic division

• Long division

• Multiplication

• Addition