Asymptotes Algebraically

• No horizontal asymptote

Answer explanation

The horizontal asymptote of the rational function is found by comparing the degrees of the numerator and denominator. As the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients, giving y = 3/6 or 1/2

If the degree of the numerator is less than the degree of the denominator in a rational function, what is the horizontal asymptote?

• The leading coefficient of the numerator divided by the leading coefficient of the denominator

• No horizontal asymptote

Answer explanation

The horizontal asymptote of a rational function where the degree of the numerator is less than the degree of the denominator is y = 0.

• No horizontal asymptote

Answer explanation

The function does not have a horizontal asymptote because the degree of the numerator is greater than the degree of the denominator, leading to no horizontal asymptote.

If the degree of the numerator and the degree of the denominator are the same, how do you find the horizontal asymptote of a rational function?

• By dividing the leading coefficients of the numerator and denominator

• The horizontal asymptote does not exist

Answer explanation

By dividing the leading coefficients of the numerator and denominator to find the horizontal asymptote.

• No horizontal asymptote

Answer explanation

The horizontal asymptote of the function is y = 0 because the degree of the numerator is less than the degree of the denominator, leading to a horizontal asymptote at y = 0.

If a rational function has a numerator degree greater than the denominator degree, what can be said about the horizontal asymptote?

• It does not exist

• It is determined by the ratio of the leading coefficients

Answer explanation

If a rational function has a numerator degree greater than the denominator degree, the horizontal asymptote does not exist.

• There are no vertical asymptotes

When identifying a vertical asymptote or hole, what variable do we use?

• x

• y

• none

• the same as the problem

When identifying a horizontal asymptote, what variable do we use?

• x

• y

• none

• the same as the problem

• y = -7

• x = 7

• y = 0

• x = -7