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frenkie
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is y=sin(x) the end behavior of y=sin(x/2)?
frenkie said:is the end behavior of sin(x/2) = sin(x) because the function settles on that equation...and i have no idea why it is oscillatory? care to explain?
also, are there any interesting points in the graph of sin(x/2)...i think the teacher is asking for asymptotes, holes and etc...which don't exist in sin(x/2)..correct?
J77 said:
The behaviour of trig fns like sine is fundamental!
Have a look on mathworld or such.
(btw: in answer to your last question - zero at 0, 2n\pi, \pi\in\mathbb{Z}, diff to find extrema etc...)
benorin said:And no, there are no other points of interest.
J77 said:
Thanks for the latex thing, benorin.
frenkie: is y=sin(x) the end behavior of y=sin(x/2)?
benorin: Yep, oscillatory. the function oscillates between -1 and 1.
benorin said:sin(x/2) looks just like sin(x), only its squished along the x-axis by a factor of 2.
The end behavior of y=sin(x) is that as x approaches positive or negative infinity, the y-values oscillate between -1 and 1. This means that the graph of y=sin(x) does not have a specific end behavior.
The end behavior of y=sin(x/2) is similar to y=sin(x) in that it also oscillates between -1 and 1 as x approaches infinity. However, the graph of y=sin(x/2) appears to be more compressed and has a shorter period than y=sin(x).
No, both y=sin(x/2) and y=sin(x) have the same end behavior. As x approaches positive or negative infinity, the y-values oscillate between -1 and 1 for both functions.
The end behavior of y=sin(x/2) can be determined by looking at the parent function, y=sin(x), and its end behavior. Since y=sin(x/2) is just a compressed version of y=sin(x), its end behavior will be the same.
The amplitude of y=sin(x/2) does not affect its end behavior. The end behavior is determined by the parent function, y=sin(x), and is not affected by any changes in amplitude.