Sketch the graph of the following functions. Find all vertical and horizontal asymptotes of the graph of each function. Determine intervals of increasing and decreasing, determine concavity, and locate all critical points and points of inflection. Show all special features such as cusps or vertical tangents.
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Vertical and horizontal asymptotes; intervals of increasing and decreasing; determining concavity; critical points and points of inflection; cusps and vertical tangents are investigated. The solution is detailed and well presented.