# Math Help - Finding the range of this equation problem.

1. ## 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.

Much appreciated.

2. ## Re: Finding the range of this equation problem.

Originally Posted by mattyc33
Find the range of the function y=-3sin(3x)-2
$\begin{gathered} - 1 \leqslant \sin (t) \leqslant 1 \hfill \\ - 3 \leqslant - 3\sin (t) \leqslant 3 \hfill \\ - 5 \leqslant - 3\sin (t) - 2 \leqslant 1 \hfill \\ \end{gathered}$

3. ## Re: Finding the range of this equation problem.

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] ?

4. ## How to put a range in union formation.

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.

5. ## Re: How to put a range in union formation.

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.

6. ## Re: How to put a range in union formation.

woohoo thanks.

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

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

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

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.