Quiz (Curve Sketching)

Show all work and justify each step.

(1) 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.


    


(2) Find constants and that guarantee that the graph of the function defined by will have a vertical asymptote at and a horizontal asymptote at

(3) Find all vertical tangents and cusps for each of the following functions. Justify your work.

    (a)         (b)
    
(4) Explain why the function has a vertical asymptote but no vertical tangent.
    
(5) Sketch the graph of the curve for . Show all special features such as vertical asymptotes, horizontal asymptotes, cusps, vertical tangents, and intercepts.
    

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Cite this as:
Curve Sketching Quiz
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/curve-sketching-quiz.html