How to identify the vertical and horizontal asymptotes with holes

The video tutorial explains how to identify vertical and horizontal asymptotes by setting the denominator equal to zero and simplifying to check for discontinuities and holes. It demonstrates factoring to find discontinuities and distinguishes between holes and asymptotes. The tutorial also covers finding horizontal asymptotes using the degree test, 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 identify potential discontinuities

• To calculate the slope of the line

• To find the x-intercepts

What is the significance of simplifying expressions when identifying discontinuities?

• To ensure all discontinuities are asymptotes

• To check if any discontinuities are removable holes

• To find the horizontal asymptotes

• To determine the degree of the polynomial

In the example provided, what type of discontinuity is x - 2?

• Removable hole

• Horizontal asymptote

• Point of intersection

• Vertical asymptote

How do you determine the horizontal asymptote of a rational function?

• By setting the numerator equal to zero

• By comparing the degrees of the numerator and denominator

• By finding the x-intercepts

• By factoring the denominator

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

• y = 0

• y = infinity

• y = x

• y = 1