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Math Help - Finding the range of this equation problem.

  1. #1
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    Finding the range of this equation problem.

    Find the range of the function y=-3sin(3x)-2

    I know that I can plug it in to my graphing calculator but I'm not sure like how exactly to tell what the range is =(.

    My professor wants it in union/infinity form eg. (-Infinity,-2]U(4,Infinity) which makes it even more confusing to me.

    Could someone please help?
    Much appreciated.
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  2. #2
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    Re: Finding the range of this equation problem.

    Quote Originally Posted by mattyc33 View Post
    Find the range of the function y=-3sin(3x)-2
    \begin{gathered}   - 1 \leqslant \sin (t) \leqslant 1 \hfill \\   - 3 \leqslant  - 3\sin (t) \leqslant 3 \hfill \\   - 5 \leqslant  - 3\sin (t) - 2 \leqslant 1 \hfill \\ \end{gathered}
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  3. #3
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    Re: Finding the range of this equation problem.

    Quote Originally Posted by Plato View Post
    \begin{gathered}   - 1 \leqslant \sin (t) \leqslant 1 \hfill \\   - 3 \leqslant  - 3\sin (t) \leqslant 3 \hfill \\   - 5 \leqslant  - 3\sin (t) - 2 \leqslant 1 \hfill \\ \end{gathered}
    Oh =) that is quite easy, suprised I didnt know that, I think what's confusing me is the notation that my prof. would like me to use

    Would it just be something like [-5,-3sin(x)-2]U[-3sin(x)-2,1] ?
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  4. #4
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    How to put a range in union formation.

    How can I put:


    Into union notation?
    Would it be [-5,-3sin(t)-2]U[-3sin(t)-2,1] ?
    Much appreciated.
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  5. #5
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    Re: How to put a range in union formation.

    Quote Originally Posted by mattyc33 View Post
    How can I put:


    Into union notation?
    Would it be [-5,-3sin(t)-2]U[-3sin(t)-2,1] ?
    Much appreciated.
    The range is [-5,1].
    There is no union about it.
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  6. #6
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    Re: How to put a range in union formation.

    woohoo thanks.
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  7. #7
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    Re: Finding the range of this equation problem.

    Quote Originally Posted by mattyc33 View Post
    Oh =) that is quite easy, suprised I didnt know that, I think what's confusing me is the notation that my prof. would like me to use

    Would it just be something like [-5,-3sin(x)-2]U[-3sin(x)-2,1] ?
    no.

    -5 \le y \le 1

    in interval notation, [-5,1]

    Interval Notation
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  8. #8
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    Re: How to put a range in union formation.

    Quote Originally Posted by mattyc33 View Post
    How can I put:


    Into union notation?
    Would it be [-5,-3sin(t)-2]U[-3sin(t)-2,1] ?
    Much appreciated.
    Do you understand what the "range" of a function is? It cannot depend on the variable as this "answer" does.
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