anonymous
  • anonymous
how do you find the range and y intercept of y=3sin(2x)+2
Mathematics
jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
to find the y intercept, plug in x = 0 and evaluate
anonymous
  • anonymous
y=2?
jim_thompson5910
  • jim_thompson5910
yes

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jim_thompson5910
  • 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
  • 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
  • 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
  • anonymous
Just to clarify, we must assume always that -1
jim_thompson5910
  • 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
  • jim_thompson5910
|dw:1444537353436:dw|
anonymous
  • anonymous
and how would we find the range?
jim_thompson5910
  • 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
  • anonymous
alright so it would be (-1,5)
jim_thompson5910
  • jim_thompson5910
[-1,5] actually
jim_thompson5910
  • jim_thompson5910
we're including the two endpoints
anonymous
  • anonymous
ok, and why are we adding 2 on both sides? I missed that
jim_thompson5910
  • 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
  • anonymous
ok
jim_thompson5910
  • jim_thompson5910
make sense?
anonymous
  • anonymous
yep I just need to review it! Thanks again Jim :)
jim_thompson5910
  • jim_thompson5910
no problem
anonymous
  • anonymous
:-)

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