When do we have an oblique, slant asymptote for a rational function

The video tutorial reviews vertical and horizontal asymptotes, explaining conditions based on the degrees of polynomials. It introduces slant (or oblique) asymptotes, detailing when they occur and how to calculate them using polynomial division, specifically long division, without considering remainders.

What condition must be met for a vertical asymptote to exist in a rational function?

• The denominator must be zero.

• The numerator must be zero.

• The degrees of numerator and denominator must be equal.

• The degree of the numerator must be greater than the denominator.

When does a horizontal asymptote occur at y = 0?

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

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

• When the denominator is zero.

• When the degrees are equal.

Under what condition does a slant asymptote occur?

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

• When the denominator is zero.

• When the degree of the numerator is exactly one more than the denominator.

• When the degrees of numerator and denominator are equal.

What is the difference in degrees between the numerator and denominator for a slant asymptote to exist?

• 0

• 1

• 2

• 3

How is the slant asymptote determined from a rational function?

• By finding the remainder of the division.

• By setting the denominator equal to zero.

• By dividing the numerator by the denominator and using the quotient.

• By setting the numerator equal to zero.