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Home > CALC > Chapter 1 > Lesson 1.3.2 > Problem 1-117


For each part below, give an example of a function with specified attributes. Provide a sketch of each function.

  1. A function with a hole at and an asymptote at .

    Write a rational function with () in both the numerator and the denominator to make a hole at .

    Remember that vertical asymptotes are formed by zeros in the denominator.

  2. A function with asymptotes at the -axis and and a hole at .

    An asymptote at the axis is the same as having a vertical asymptote of .

  3. A function with an end behavior function .

    Holes and vertical asymptotes do not affect end behavior. How can be altered so that it has a hole or vertical asymptote?

    Possible answer: [answer to part (a)]