- anonymous

how do you find the range and y intercept of y=3sin(2x)+2

- jamiebookeater

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- jim_thompson5910

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

- anonymous

y=2?

- jim_thompson5910

yes

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## More answers

- 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
\[\Large -1 \le \sin(2x) \le 1\]

- jim_thompson5910

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

- 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)

- anonymous

Just to clarify, we must assume always that -1

- 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

- jim_thompson5910

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- anonymous

and how would we find the range?

- 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

- anonymous

alright so it would be (-1,5)

- jim_thompson5910

[-1,5] actually

- jim_thompson5910

we're including the two endpoints

- anonymous

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

- 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)

- anonymous

ok

- jim_thompson5910

make sense?

- anonymous

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

- jim_thompson5910

no problem

- anonymous

:-)

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