Master Find the Slant Asymptotes of Rational Functions

The video tutorial explains how to find slant or oblique asymptotes of rational functions. It covers the conditions under which slant asymptotes occur and demonstrates how to find them using division. The tutorial includes examples with monomial and binomial denominators, showing both long division and synthetic division methods. It emphasizes the importance of understanding the division process and provides step-by-step guidance for solving complex problems.

What condition must be met for a rational function to have a slant asymptote?

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

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

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

• The degrees of the numerator and denominator are both zero.

When dividing a polynomial by a monomial, what is the simplest method to find the slant asymptote?

• Use synthetic division.

• Graph the function directly.

• Divide each term of the numerator by the monomial.

• Use the quadratic formula.

In long division, why is it important to use parentheses when subtracting rows?

• To avoid using synthetic division.

• To simplify the polynomial.

• To make the division process faster.

• To ensure the correct subtraction of each term.

What is the remainder when using long division to find a slant asymptote?

• It is always zero.

• It is ignored when determining the slant asymptote.

• It is added to the quotient.

• It is subtracted from the quotient.

How do you determine the quotient in long division when the divisor is a binomial?

• Subtract the divisor from the dividend.

• Add the divisor to the dividend.

• Multiply the entire dividend by the divisor.

• Divide the first term of the dividend by the first term of the divisor.

Why is it important to ensure the dividend and divisor are in descending order of powers in long division?

• To ensure accurate subtraction of terms.

• To simplify the multiplication process.

• To avoid errors in synthetic division.

• To make the division process faster.

What is a key requirement for using synthetic division?

• The divisor must have a higher degree than the dividend.

• The dividend must be a quadratic polynomial.

• The divisor must be a linear binomial.

• The divisor must be a monomial.

Why can't synthetic division be used when the divisor is not linear?

• Because it simplifies the polynomial too much.

• Because it only applies to linear divisors.

• Because it requires the divisor to be a factor of the polynomial.

• Because it only works with monomials.

What happens to the remainder in synthetic division?

• It becomes the new divisor.

• It is used to adjust the quotient.

• It is ignored for the purpose of finding the slant asymptote.

• It is added to the dividend.

In the context of slant asymptotes, what is the significance of the quotient obtained from division?

• It represents the vertical asymptote.

• It is the equation of the slant asymptote.

• It is the remainder of the division.

• It is used to find the x-intercepts.