## anonymous one year ago how do you find the range and y intercept of y=3sin(2x)+2

1. jim_thompson5910

to find the y intercept, plug in x = 0 and evaluate

2. anonymous

y=2?

3. jim_thompson5910

yes

4. jim_thompson5910

the range of sin(x) spans from -1 to +1 in other words, $\Large -1 \le \sin(x) \le 1$ the x can be replaced with anything you want, so let's replace x with 2x $\Large -1 \le \sin(2x) \le 1$

5. jim_thompson5910

we can then multiply every side by 3 $\Large -1*3 \le 3*\sin(2x) \le 3*1$ $\Large -3 \le 3\sin(2x) \le 3$

6. jim_thompson5910

and then finally add to 2 all sides $\Large -3+2 \le 3\sin(2x)+2 \le 3+2$ $\Large -1 \le 3\sin(2x)+2 \le 5$ so the range of y = 3*sin(2x)+2 spans from -1 to +5 (including both endpoints)

7. anonymous

Just to clarify, we must assume always that -1<sin(x)<1?

8. jim_thompson5910

yes sin(x) is a function that bounces up and down. It doesn't go past y = 1 or y = -1. It's boxed in so to speak in terms of the y direction

9. jim_thompson5910

|dw:1444537353436:dw|

10. anonymous

and how would we find the range?

11. jim_thompson5910

do you see my steps above and how they led to $$\LARGE \Large -1 \le 3\sin(2x)+2 \le 5$$ all that work shows how to find the range for y = 3sin(2x)+2

12. anonymous

alright so it would be (-1,5)

13. jim_thompson5910

[-1,5] actually

14. jim_thompson5910

we're including the two endpoints

15. anonymous

ok, and why are we adding 2 on both sides? I missed that

16. jim_thompson5910

because we initially had just 3sin(2x) in the middle (without the +2) adding 2 to all sides will have 3sin(2x)+2 in the middle (now with the +2)

17. anonymous

ok

18. jim_thompson5910

make sense?

19. anonymous

yep I just need to review it! Thanks again Jim :)

20. jim_thompson5910

no problem

21. anonymous

:-)