Finding the range of this equation problem.

**mattyc33** · September 22nd 2011, 11:48 AM

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.

**Plato** · September 22nd 2011, 11:56 AM

Originally Posted by mattyc33

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

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

**mattyc33** · September 22nd 2011, 12:14 PM

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] ?

**mattyc33** · September 22nd 2011, 12:58 PM

How can I put:
$\begin{gathered} - 1 \leqslant \sin (t) \leqslant 1 \hfill \\ - 3 \leqslant - 3\sin (t) \leqslant 3 \hfill \\ - 5 \leqslant - 3\sin (t) - 2 \leqslant 1 \hfill \\ \end{gathered}$

Into union notation?
Would it be [-5,-3sin(t)-2]U[-3sin(t)-2,1] ?
Much appreciated.

**Plato** · September 22nd 2011, 01:18 PM

Originally Posted by mattyc33

How can I put:
$\begin{gathered} - 1 \leqslant \sin (t) \leqslant 1 \hfill \\ - 3 \leqslant - 3\sin (t) \leqslant 3 \hfill \\ - 5 \leqslant - 3\sin (t) - 2 \leqslant 1 \hfill \\ \end{gathered}$

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.

**mattyc33** · September 22nd 2011, 01:20 PM

woohoo thanks.

**skeeter** · September 22nd 2011, 04:55 PM

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

**HallsofIvy** · September 23rd 2011, 07:55 AM

Originally Posted by mattyc33

How can I put:
$\begin{gathered} - 1 \leqslant \sin (t) \leqslant 1 \hfill \\ - 3 \leqslant - 3\sin (t) \leqslant 3 \hfill \\ - 5 \leqslant - 3\sin (t) - 2 \leqslant 1 \hfill \\ \end{gathered}$

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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