Horizontal and Vertical Asymptotes

This video tutorial explains how to find vertical and horizontal asymptotes and identify holes in rational functions. It covers the steps and rules for determining horizontal asymptotes based on the degrees of the numerator and denominator. Examples are provided to illustrate these concepts. The video also details the process of finding vertical asymptotes by factoring equations and setting the denominator equal to zero. Additionally, it explains how to identify holes when terms cancel out in the numerator and denominator, and how to find the coordinates of these holes.

What is the first step in finding a horizontal asymptote?

• Divide the leading coefficients

• Set the denominator equal to zero

• Factor the equation

• Find the highest degree in the numerator and denominator

If the degree of the numerator is less than the degree of the denominator, what is the horizontal asymptote?

• No horizontal asymptote

• Divide the leading coefficients

• y = 1

• y = 0

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

• Set the denominator equal to zero

• Divide the leading coefficients

• There is no horizontal asymptote

• y = 0

In the example where the highest degree on top is 3 and the highest degree on the bottom is 2, what is the horizontal asymptote?

• No horizontal asymptote

• Divide the leading coefficients

• y = 3/2

• y = 0

For the function f(x) = (x - 1) / (x² + 5x + 6), what is the horizontal asymptote?

• y = 1/2

• No horizontal asymptote

• y = 0

• y = 1

What is the horizontal asymptote for the function 3x² - 5 / 4x² + 6?

• y = 3/4

• y = 0

• No horizontal asymptote

• y = 1

What is the first step in finding vertical asymptotes?

• Factor the equation

• Divide the leading coefficients

• Find the highest degree in the numerator and denominator

• Set the numerator equal to zero

How do you find vertical asymptotes after factoring the equation?

• Set the numerator equal to zero

• Divide the leading coefficients

• Set the denominator equal to zero

• Find the highest degree in the numerator and denominator

In the example x² - 16 / x² + 2x - 24, what is the vertical asymptote?

• x = 4

• x = -4

• x = 6

• x = -6

How do you identify a hole in the function?

• When the degrees of the numerator and denominator are equal

• When the numerator is greater than the denominator

• When a factor cancels out in the numerator and denominator

• When the denominator is set to zero