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Math Help - range of graph

  1. #1
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    range of graph

    Hello, I have graphed the following equation:
    y= 1/(x-1)

    and I have figured out the domain (-infinity,1) U (1, +infinity), but I don't know what the range is and how to get it?
    I know some main points as (2,1) and (-1, -.5) and (0,-1).
    Thank you!
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  2. #2
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    Quote Originally Posted by ss103 View Post
    Hello, I have graphed the following equation:
    y= 1/(x-1)

    and I have figured out the domain (-infinity,1) U (1, +infinity), but I don't know what the range is and how to get it?
    I know some main points as (2,1) and (-1, -.5) and (0,-1).
    Thank you!
    The range is \mathbf{R}\backslash\{0\}.

    You can easily check this by noting that if you let y=0 you can not solve for x.
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  3. #3
    Senior Member pacman's Avatar
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    asymtotic to x =1, as stated above. take a look at the graph
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  4. #4
    Senior Member pacman's Avatar
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    y = 1/(x - 1), at x = 1, y is undefined. Better graph below,
    Attached Thumbnails Attached Thumbnails range of graph-ok.gif  
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  5. #5
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    thanks! so is the range (-infinity,0) U (0, +infinity) ?
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  6. #6
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    Quote Originally Posted by ss103 View Post
    Hello, I have graphed the following equation:
    y= 1/(x-1)

    and I have figured out the domain (-infinity,1) U (1, +infinity), but I don't know what the range is and how to get it?
    sometimes, a good way to find the range of a function is to find the domain of the function's inverse ...

    y = \frac{1}{x-1}

    x = \frac{1}{y-1}

    y-1 = \frac{1}{x}

    y = \frac{1}{x} + 1

    domain of the inverse = range of the original function is all reals except 0
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