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

  1. A function with a hole at x = 3 and an asymptote at x = −1.

    Write a rational function with (x − 3) in both the numerator and the denominator to make a hole at x = 3.

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

  2. A function with asymptotes at the y-axis and x = 5 and a hole at x = −4.

    An asymptote at the x axis is the same as having a vertical asymptote of x = 0.

  3. A function with an end-behavior function g(x) = 3x − 1.

    Holes and vertical asymptotes do not affect end behavior. How can y = 3x − 1 be altered so that it has a hole or vertical asymptote?

    Possible answer: y = 3x − 1 + [answer to part (a)].