Finding Horizontal and Vertical Asymptotes in Rational Functions

What is the first step in analyzing horizontal asymptotes?

• Compare the degrees of the numerator and denominator

• Factor the numerator

• Look at the coefficients of the terms

• Factor the denominator

If the degree of the denominator is higher than the numerator, what does the horizontal asymptote approach?

• y = infinity

• y = x

• y = 0

• y = 1

When the degrees of the numerator and denominator are the same, how do you determine the horizontal asymptote?

• By multiplying the coefficients

• By dividing the coefficients

• By subtracting the coefficients

• By adding the coefficients

What type of asymptote is formed when the degree of the numerator is greater than the degree of the denominator?

• No asymptote

• Vertical asymptote

• Horizontal asymptote

• Slant asymptote

How do you find the equation of a slant asymptote?

• By factoring the denominator

• By polynomial long division

• By factoring the numerator

• By comparing the coefficients

What should you do to find vertical asymptotes?

• Factor the numerator and denominator

• Add the coefficients of the highest degree terms

• Compare the degrees of the numerator and denominator

• Perform polynomial long division

What happens if a factor in the denominator cancels with a factor in the numerator?

• A slant asymptote is formed

• A removable discontinuity is formed

• A horizontal asymptote is formed

• A vertical asymptote is formed

If x = -3 is a factor in the denominator but not in the numerator, what type of asymptote is formed?

• Horizontal asymptote

• Vertical asymptote

• Slant asymptote

• No asymptote

What is a removable discontinuity?

• A vertical asymptote

• A point where the graph is undefined

• A horizontal asymptote

• A slant asymptote

What is the key step to identify removable discontinuities?

• Factoring the numerator and denominator and canceling common factors

• Comparing the degrees of the numerator and denominator

• Adding the coefficients of the highest degree terms

• Performing polynomial long division