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

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5to find the y intercept, plug in x = 0 and evaluate

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5the 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
 one year ago
Best ResponseYou've already chosen the best response.5we 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
 one year ago
Best ResponseYou've already chosen the best response.5and 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
 one year ago
Best ResponseYou've already chosen the best response.0Just to clarify, we must assume always that 1<sin(x)<1?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5yes 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
 one year ago
Best ResponseYou've already chosen the best response.5dw:1444537353436:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and how would we find the range?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5do 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
 one year ago
Best ResponseYou've already chosen the best response.0alright so it would be (1,5)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5[1,5] actually

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5we're including the two endpoints

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok, and why are we adding 2 on both sides? I missed that

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5because 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
 one year ago
Best ResponseYou've already chosen the best response.0yep I just need to review it! Thanks again Jim :)
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