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Horizontal and Vertical Asymptotes

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September 10th, 2022

1. How do you determine the vertical asymptotes, given the equation of a rational function? Illustrate with an example. Why can’t the graph of that function cross the assymptote? Describe what happens to the graph of a function as the value of the independent variable approaches its vertical asymptote.

2. How do you determine the horizontal asymptotes, given the equation of a rational function? If you let x take on very large positive values, and very small negative values, what can this tell you about the far right and left sides of the graph of a rational function that has horizontal asymptotes?

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