How to identify vertical and horizontal asymptotes with holes

The video tutorial explains how to find vertical and horizontal asymptotes by setting the denominator equal to zero and using the degree test. It emphasizes the importance of simplifying expressions to identify discontinuities and holes. The process of factoring is used to determine which discontinuities are holes and which are asymptotes. The tutorial concludes with a method to find horizontal asymptotes by comparing the degrees of the numerator and denominator.

Why is it important to set the denominator equal to zero when finding vertical asymptotes?

• To determine the y-intercepts

• To find the x-intercepts

• To calculate the slope of the line

• To identify potential discontinuities

What is the significance of simplifying expressions when identifying discontinuities?

• To determine the degree of the polynomial

• To find the horizontal asymptotes

• To check if any discontinuities are removable holes

• To ensure all discontinuities are asymptotes

In the example provided, why is x - 2 considered a hole?

• Because it is a horizontal asymptote

• Because it is a non-removable discontinuity

• Because it is a vertical asymptote

• Because it is a removable discontinuity

How do you determine the horizontal asymptote using the degree test?

• By setting the denominator equal to zero

• By comparing the coefficients of the highest degree terms

• By comparing the degrees of the numerator and denominator

• By setting the numerator equal to zero

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

• Y equals infinity

• Y equals 0

• Y equals the leading coefficient

• Y equals 1