Master How to determine the vertical asymptotes of a rational function

The video tutorial explains how to determine vertical asymptotes in rational functions. It covers the process of setting the denominator equal to zero to find values not in the domain, which may create holes or asymptotes. The tutorial provides examples, discusses simplification, and addresses non-factorable denominators and imaginary solutions. It also explains how to identify holes in graphs and their impact on the domain.

What is the first step in finding the domain of a rational function?

• Set the numerator equal to zero

• Set the denominator equal to zero

• Add the numerator and denominator

• Multiply the numerator and denominator

How can you identify a hole in a rational function?

• By setting the denominator equal to zero

• By multiplying the numerator and denominator

• By dividing out a common factor in the numerator and denominator

• By setting the numerator equal to zero

What happens if you set the denominator equal to zero and find no real solutions?

• The function has a horizontal asymptote

• The function has a hole

• The function is undefined

• There are no vertical asymptotes

In the example X / (X^2 + 3), why are there no vertical asymptotes?

• Because the numerator and denominator are equal

• Because the solutions are imaginary

• Because the denominator is not factorable

• Because the numerator is zero

What should you do if you can factor the denominator of a rational function?

• Ignore the factors

• Set each factor equal to zero

• Multiply the factors

• Add the factors

What does an open circle on a graph of a rational function represent?

• A horizontal asymptote

• A hole

• A vertical asymptote

• A point of intersection

When simplifying a rational function, what indicates the presence of a hole?

• An imaginary number

• A zero in the denominator

• A zero in the numerator

• A common factor in the numerator and denominator