Question 1110177: True or false: y=3x-2sin2x oscillates between the parallel lines y=3x-4 and y=3x+4
I know the maximum value a sine function can have is one, so
y=3x-2sin2x is really y=3x-2(1), which is y=3x-2, which makes the statement false.
However, the amplitude in this case is 2, so:
y=3x-2sin2x is really y=3x-2(2), which is y=3x-4, which makes the statement true.
Found 2 solutions by greenestamps, Alan3354:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
No.
sin(x), sin(2x), and sin(kx) (for any value of k) all have maximum and minimum values of 1 and -1.
Specifically, it is NOT true that sin(2x) has an amplitude of 2.
Since sin(2x) has an amplitude of 1, 2sin(2x) has an amplitude of 2; so 3x-2sin(2x) oscillates between 3x-2 and 3x+2.
So the statement that it oscillates between 3x-4 and 3x+4 is false.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! True or false: y=3x-2sin2x oscillates between the parallel lines y=3x-4 and y=3x+4
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"oscillates between" is subject to interpretation.
All values of the function are surrounded by the 2 linear functions, but there is no contact, no common points.
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DL the FREE graph software at
www.padowan.dk and see it.
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Use Ins, then enter 3x - 2sin(2x), any color.
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