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Math Help - Domain and Range

  1. #1
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    Domain and Range

    Alright, I'm having trouble with these concepts.

    Well, figuring out the range. I've used like three books and haven't really understood it.

    I know how to find out the domain. It'll either be like any real number or like -3 less than or equal to 0 less than or equal to 3. Something like that.

    But the range, I think, you can find on the y-axis. Like say that example and the function or line crosses the y-axis at 0. How would I write that?

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  2. #2
    Member eXist's Avatar
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    Domain is essentially what values are applicable(valid) for x.

    Ex: \frac{x + 1}{x - 1}
    In this case the domain is:
    x = \epsilon (All real numbers)
    x \ne 1

    There is a vertical asymptote at 1.

    Range is essentially what values are applicable(valid) for y.

    Ex: \frac{x + 1}{x - 1}
    In this case the domain is:
    y = \epsilon (All real numbers)
    y \ne 1

    There is a horizontal asymptote at 1.

    For more info:
    Domain of a function - Wikipedia, the free encyclopedia
    Range (mathematics) - Wikipedia, the free encyclopedia
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  3. #3
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    Well, what if there isn't anything like that? I know how to do it like that.

    Like the picture I posted. It's just a graph and I'm suppose to find the range.
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  4. #4
    Member eXist's Avatar
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    On your graph specifically we can see that x extends in the negative and positive direction infinitely.
    So the domain of x: x = \epsilon (All real numbers)

    Similar problem for the range. On your graph (I can't really see the markings on the graph) but I'm assuming it's a sin function.
    For simplicities sake I'm going to assume it's: f(x) = sinx

    That means that the range of y is simply the range of the function: f(x) = sinx. And the range is: |y| \le 1

    Now, on your graph, you have to check what numbers it's oscillating between.
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  5. #5
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    Quote Originally Posted by eXist View Post
    On your graph specifically we can see that x extends in the negative and positive direction infinitely.
    So the domain of x: x = \epsilon (All real numbers)

    Similar problem for the range. On your graph (I can't really see the markings on the graph) but I'm assuming it's a sin function.
    For simplicities sake I'm going to assume it's: f(x) = sinx

    That means that the range of y is simply the range of the function: f(x) = sinx. And the range is: |y| \le 1

    Now, on your graph, you have to check what numbers it's oscillating between.
    Well, it's between -5 and 5 and it might very well be a sinx whatever, but I don't think that's how it's written yet. This is just a College Algebra problem. On the graph on the y-axis the lowest and highest points would be -1 and 1.
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  6. #6
    Member eXist's Avatar
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    If the graph shows restrictions on x (like you said between -5 and 5) mark it that way. Same thing for y .
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