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Math Help - Need Help finding range of function with absolute value in denominator

  1. #1
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    Need Help finding range of function with absolute value in denominator

    I am completely stuck on this question, thanks for all help.

    I am supposed to find the domain and range of the function:

    f(x)=\frac{x}{|x|}

    I have solved the domain as (-\infty,0)\cup(0,\infty)

    It's been quite a few years since I've worked with domain and ranges, then again one with an absolute value in the denominator.

    I know that from (-\infty,0) it's a horizontal line at y=-1 and that from (o,\infty) it's a horizontal line at y=1. How do I write the range for this?
    Last edited by jester469; January 21st 2011 at 01:21 PM. Reason: Correct title
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  2. #2
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    Quote Originally Posted by jester469 View Post
    I am completely stuck on this question, thanks for all help.

    I am supposed to find the domain and range of the function:

    f(x)=\frac{x}{|x|}

    I have solved the domain as (-\infty,0)\cup(0,\infty)

    It's been quite a few years since I've worked with domain and ranges, then again one with an absolute value in the denominator.

    I know that from (-\infty,0) it's a horizontal line at y=-1 and that from (o,\infty) it's a horizontal line at y=1. How do I write the range for this?
    You just wrote it.
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  3. #3
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    Quote Originally Posted by dwsmith View Post
    You just wrote it.
    The range is the y values.
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  4. #4
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    Thank you, but how do I write the answer properly? Is it written the same as like a piecewise function?
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  5. #5
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    Quote Originally Posted by jester469 View Post
    Thank you, but how do I write the answer properly? Is it written the same as like a piecewise function?
    Yes, that is fine.
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    It's fine how you wrote it. If you wanted to write it in compact form you use set notation,
    R_{f}: \{1\} U \{-1\}
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  7. #7
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    Even more compactly, {1, -1}!
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  8. #8
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    y = \pm 1
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  9. #9
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    lol trust you guys to make a sport of compactness
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  10. #10
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    Quote Originally Posted by Krahl View Post
    lol trust you guys to make a sport of compactness
    ... it's a living.
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