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Analysis and Graphing of Rational Functions

An assignment focused on analyzing and graphing rational functions, using various mathematical techniques.

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Analysis and Graphing of Rational FunctionsGraph Sketching ProjectName:________________________Directions:Complete each of the following problems. Be sure toshow your workin order to receive full or partial credit. Youmay use your calculator, notes, and book to complete the project. Itis not appropriate to graph the function in your calculator anddetermine any of the answers based on inspection. You mustillustrate your understanding of the calculus techniques discussedin the book.Consider the functionf(x) =-5 / (x^2–36)a.Determine the intercepts of the function.

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b.Determine the vertical asymptote(s).

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c.Determine the location of any holes if theyexist (give theordered pair).

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d.Determine the horizontal asymptote.

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e.Determine the domain of the function.

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f.Find all thecritical valuesof the function if any exist.Give bothcoordinates (ordered pair).

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