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?

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

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

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

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

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

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

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