# Thread: Range of Values Question

1. ## Range of Values Question

Hi there,
Can you help me with the following problem please?

If f(x) = 2 sin(3x - pi/2) + 5, what is the range of the values of f(x)?

I began by moving 5 over to the other side.

2 sin(3x - pi/2) = - 5

sin(3x - pi/2) = -5/2

Am I going in the right direction?
Thanks
Cromlix

2. No, I wouldn't go in that direction. I would build up the function f(x) from the simpler components using inequalities, like this:

$\displaystyle -1\le\sin(3x-\pi/2)\le 1$

$\displaystyle -2\le 2\sin(3x-\pi/2)\le 2.$

How could you finish?

3. Hi Ackbeet,
Thank you for replying: I would proceed:- -1=< sin(3x - pi/2) =< 1
-2=< sin(3x - pi/2) =< 2

3=< sin(3x - pi/2) =< 7 Cheers, Cromlix

4. Right idea, but your notation is off on the last line. You want

$\displaystyle 3\le\sin(3x - \pi/2)+5 \le 7.$