Finding the Slant Asymptote

The video tutorial explains how to find vertical, horizontal, and slant asymptotes in rational functions. It begins with identifying vertical asymptotes by setting the denominator equal to zero. Then, it covers horizontal asymptotes, determined by comparing the degrees of the numerator and denominator polynomials. If the numerator's degree is higher, a slant asymptote is present, which is found using long division. The tutorial emphasizes understanding graph behavior near these asymptotes.

What is the condition for a vertical asymptote in a rational function?

• The numerator is greater than the denominator.

• The numerator equals zero.

• The denominator equals zero.

• The degrees of numerator and denominator are equal.

When does a rational function have a horizontal asymptote at y = 0?

• When the numerator equals zero.

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

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

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

What is a slant asymptote?

• An asymptote that occurs when the numerator equals zero.

• An asymptote that occurs when the degree of the numerator is less than the degree of the denominator.

• An asymptote that occurs when the degree of the numerator is greater than the degree of the denominator.

• An asymptote that occurs when the degrees of the numerator and denominator are equal.

Why is long division used to find slant asymptotes?

• Because it is the only method for finding vertical asymptotes.

• Because it is faster than synthetic division.

• Because it simplifies the numerator.

• Because it can handle non-factorable polynomials.

What must be ensured when performing long division to find a slant asymptote?

• All terms in the numerator are represented.

• The numerator is greater than the denominator.

• The denominator is a factor of the numerator.

• The remainder is zero.

What happens to the remainder when finding a slant asymptote using long division?

• It is added to the final result.

• It is ignored.

• It determines the vertical asymptote.

• It is used to find the horizontal asymptote.

What is the result of the long division used to find a slant asymptote?

• The sum of the numerator and denominator.

• The product of the divisor and quotient.

• The quotient without the remainder.

• The remainder of the division.