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Math Help - Graphing function and its reciprocal, also get domain/range

  1. #1
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    Graphing function and its reciprocal, also get domain/range

    Hello.

    I have the function y=x^2 - 3
    Would the reciprocal be: y= 1/(x^2-3)?

    (I need to graph these by hand without a graphing calculator.)

    Now how would I graph y=x^2-3?
    The -3 tells me the min of the range is -3? So I start at -3 and go up, but how do I know how wide to make it or where to make the zeroes?

    Same thing for the reciprocal, I have no idea to graph that and find the range/domains of it too.

    Any help would be greatly appreciated.
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  2. #2
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    Quote Originally Posted by olen12 View Post
    Hello.

    I have the function y=x^2 - 3
    Would the reciprocal be: y= 1/(x^2-3)?

    (I need to graph these by hand without a graphing calculator.)

    Now how would I graph y=x^2-3?
    The -3 tells me the min of the range is -3? So I start at -3 and go up, but how do I know how wide to make it or where to make the zeroes?

    Same thing for the reciprocal, I have no idea to graph that and find the range/domains of it too.

    Any help would be greatly appreciated.
    The function y=x^2-3 is simply the same thing as y=x^2, a parabola that has shifted down the y axis three units.
    So just graph x^2 and slide it down.

    The function y=\frac{1}{x^2-3} is simply a hyperbola. Whenever dealing with hyperbolas, always look for vertical asymptotes. i.e. where the function is undefined. Theses will help you sketch the graph.
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