Horizontal Asymptotes in Functions

This video tutorial explains how to find horizontal asymptotes of rational functions by considering three cases based on the degrees of the numerator and denominator. It covers when the asymptote is zero, when it is the ratio of leading coefficients, and when there is no horizontal asymptote. The video also introduces oblique asymptotes and provides examples and practice problems to reinforce the concepts.

What is the horizontal asymptote when the degree of the numerator is less than the degree of the denominator?

• Zero

• One

• Undefined

• Infinity

If the degrees of the numerator and denominator are equal, how do you find the horizontal asymptote?

• Multiply the coefficients

• Subtract the coefficients

• Add the coefficients

• Divide the leading coefficients

What happens to the horizontal asymptote if the degree of the numerator is greater than the degree of the denominator?

• There is no horizontal asymptote

• It is undefined

• It is zero

• It is infinity

For the function f(x) = 1/x, what is the horizontal asymptote?

• 1

• 0

• x

• Undefined

In the function f(x) = 7/(x-5), what is the horizontal asymptote?

• Undefined

• 0

• 5

• 7

For the function f(x) = 7/(x^2 - 16) - 7, what is the horizontal asymptote?

• 7

• Undefined

• 0

• -7

What is the horizontal asymptote for f(x) = (2x - 3)/(x - 16)?

• 2

• 3

• 0

• 1

For the function f(x) = (12x - 6)/(3x + 4) + 5, what is the horizontal asymptote?

• 4

• 5

• 9

• 6

What type of asymptote does f(x) = (x^2 + 5x + 6)/(x + 3) have?

• Horizontal

• Oblique

• None

• Vertical

For the function f(x) = (2x^2 - 8x + 6)/(x^2 + 4), what is the horizontal asymptote?

• Undefined

• 0

• 1

• 2