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Math Help - Graph of a rational function

  1. #1
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    Graph of a rational function

    How would I graph the following rational function with the following properties?


    • f is defined for all real numbers except 3 and -3
    • f is an even function
    • f(1) = 0, and f(0) = -3/2
    • as x -> infinity, f(x) -> 2
    • as x -> 3^-, f(x) -> infinity, and as x -> 3^+, f(x) -> -infinity

    Any help would be appreciated, thanks!
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  2. #2
    Senior Member vincisonfire's Avatar
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    Reply

    - You have a vertical asymptote at x=-3 and one at x=3.
    - An even function is symmetric with respect to y-axis.
    - You probably know how to plot points.
    - There is an asymptote at x = 2 the function may or may not cross it but we must see that y goes to 2 as x goes to infinity.
    - On the left of x = 3 asymptote, y goes to infinity and on the left it comes from -infinity.
    - Because of symmetry, it is the opposite for x = -3 asymptote.
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