Finding the range of this equation problem.

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September 22nd 2011, 11:48 AM
mattyc33

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.
September 22nd 2011, 11:56 AM
Plato

Re: Finding the range of this equation problem.

Quote:

Originally Posted by mattyc33

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

$\begin{gathered} - 1 \leqslant \sin (t) \leqslant 1 \hfill \\ - 3 \leqslant - 3\sin (t) \leqslant 3 \hfill \\ - 5 \leqslant - 3\sin (t) - 2 \leqslant 1 \hfill \\ \end{gathered}$
September 22nd 2011, 12:14 PM
mattyc33

Re: Finding the range of this equation problem.

Quote:

Originally Posted by Plato

$\begin{gathered} - 1 \leqslant \sin (t) \leqslant 1 \hfill \\ - 3 \leqslant - 3\sin (t) \leqslant 3 \hfill \\ - 5 \leqslant - 3\sin (t) - 2 \leqslant 1 \hfill \\ \end{gathered}$

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] ?
September 22nd 2011, 12:58 PM
mattyc33

How to put a range in union formation.

How can I put:
http://latex.codecogs.com/png.latex?...\end{gathered}

Into union notation?
Would it be [-5,-3sin(t)-2]U[-3sin(t)-2,1] ?
Much appreciated.
September 22nd 2011, 01:18 PM
Plato

Re: How to put a range in union formation.

Quote:

Originally Posted by mattyc33

How can I put:
http://latex.codecogs.com/png.latex?...\end{gathered}

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.
September 22nd 2011, 01:20 PM
mattyc33

Re: How to put a range in union formation.

woohoo thanks.
September 22nd 2011, 04:55 PM
skeeter

Re: Finding the range of this equation problem.

Quote:

Originally Posted by mattyc33

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
September 23rd 2011, 07:55 AM
HallsofIvy

Re: How to put a range in union formation.

Quote:

Originally Posted by mattyc33

How can I put:
http://latex.codecogs.com/png.latex?...\end{gathered}

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.