What is a slant asymptote

The video tutorial explains vertical, horizontal, and slant asymptotes. It focuses on slant asymptotes, which occur when the degree of the numerator is greater than the degree of the denominator in a rational function. The tutorial demonstrates how to find slant asymptotes using long division, emphasizing that the remainder approaches zero as it goes to infinity. The slant asymptote is represented by a linear equation with a slope, unlike horizontal asymptotes, which have a slope of zero.

What is a vertical asymptote?

• A line that a function approaches horizontally

• A line that a function never crosses

• A line that a function approaches vertically

• A point where the function is undefined

When do slant asymptotes occur in a rational function?

• 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

• When the function has no vertical asymptotes

How do you find the slant asymptote of a rational function?

• By setting the numerator equal to zero

• By using long division to divide the numerator by the denominator

• By calculating the derivative of the function

• By finding the horizontal asymptote first

What happens to the remainder when finding a slant asymptote?

• It affects the horizontal asymptote

• It determines the vertical asymptote

• It is ignored as it approaches zero

• It becomes the slant asymptote

What is the equation of a slant asymptote if the quotient is x?

• y = x^2

• y = x

• y = 0

• y = 1/x