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Math Help - Set Notation for Domain and Range

  1. #1
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    Set Notation

    Using some form of set notation, indicate the domain and range of each function defined below:

    f(x)=-3x^2 Domain: Range


    f(x)= 5x-7 Domain: Range:



    f(x)= -2
    ________
    7 - x

    Domain: Range:
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  2. #2
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    Quote Originally Posted by batman123
    Using some form of set notation, indicate the domain and range of each function defined below:

    f(x)=-3x^2 Domain: Range


    f(x)= 5x-7 Domain: Range:



    f(x)= -2
    ________
    7 - x

    Domain: Range:
    Notice that the function,
    f(x)=-3x^2 has a meaning for any x. Now you want it in set notation, one way is to write x\in \mathbb{R} implying that x is any REAL number. Another way is to assign the interval x\in (-\infty,\infty). Meaning x could be as small as you wish and as large as you wish. Now the range is the y value, notice that -3x^2 is always a negative number thus, y \in [0,\infty). Notice the square bracket indicating that y can be equal to 0 which is true.

    The function f(x)=5x-7 is defined for any x thus we write x\in (-\infty,\infty) (let me just remind you then infinity is not a number even I use it does not mean that it is). If you graph this line you will see the the y value is anything thus we write y\in (-\infty,\infty).

    The function f(x)=\frac{-2}{7-x} is not defined for all x it is undefined for x=0 thus, x cannot be 0, thus we write (this might be tricky) x\in (-\infty,0)\cup (0,\infty)- the circle bracket indicate x\not =0 which we are trying to state. If you graph this function, you will see the y always has a value except for y=0 (because the equation 0=\frac{-2}{7-x} has not solution). But besides for that y always has a value thus we write, y\in (-\infty,0)\cup(0,\infty).

    Let me give you a more challenging one,
    y=\sqrt{\frac{1}{x}}
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ThePerfectHacker
    notice that -3x^2 is always a negative number thus, y \in [0,\infty)
    Got a little "oopsie" here. This should be "notice that -3x^2 is never a positive number thus, y \in (- \infty,0].

    -Dan

    (Hey, usually I'm the guy getting the set notation wrong! )
    Last edited by topsquark; March 5th 2006 at 03:53 PM. Reason: typo
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    Wink Thanks!

    Thanks Guys
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    Quote Originally Posted by topsquark
    Got a little "oopsie" here. This should be "notice that -3x^2 is never a positive number thus, y \in (- \infty,0].

    -Dan

    (Hey, usually I'm the guy getting the set notation wrong! )
    I always thought I was Perfect, now you showed that even I am able to make mistakes.
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  6. #6
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    Quote Originally Posted by ThePerfectHacker
    ...

    The function f(x)=\frac{-2}{7-x} is not defined for all x it is undefined for x=0 thus, ...
    Hello,

    ... it is undefined for 7-x=0 because the division by zero is not allowed. Thus the domain is \Re \setminus \{ 7 \}

    Greetings

    EB
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  7. #7
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    Quote Originally Posted by earboth
    Hello,

    ... it is undefined for 7-x=0 because the division by zero is not allowed. Thus the domain is \Re \setminus \{ 7 \}

    Greetings

    EB
    The usual symbol for the reals is \mathbb{R} obtained with
    the TeX string "\mathbb{R}".

    RonL
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  8. #8
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    Quote Originally Posted by CaptainBlack
    The usual symbol for the reals is \mathbb{R} obtained with
    the TeX string "\mathbb{R}".

    RonL
    Hello,

    Thanks for your hint. I've taken the symbol which I found in the "Latex-manual" of the forum. Maybe it would be nice to add those symbols to this manual. (Are there any \matbb{N}, or \mathbb{Z}, or ... too?)

    Once again: Thanks.

    Greetings

    EB
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