Why Some Rational Functions Have No Vertical Asymptote

The video tutorial explores rational expressions that do not have vertical asymptotes, addressing common student misconceptions. It provides three examples: simplifying rational expressions, identifying removable discontinuities, and using complex numbers to explain the absence of vertical asymptotes. The tutorial emphasizes the importance of understanding when a function is undefined and how this relates to vertical asymptotes.

What is a vertical asymptote and how does it relate to rational expressions?

Explain why the expression 1/x has a vertical asymptote.

What happens to the vertical asymptote when the denominator of a rational expression is modified?

How can you determine if a rational expression has vertical asymptotes?

Describe the difference between a vertical asymptote and a removable discontinuity.

In the context of rational expressions, explain what is meant by a 'hole' in the graph.

What is the significance of the values that make the denominator equal to zero in rational expressions?