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Question 752974: I am trying to find the amplitude and period for this function (if you can also describe a bit of what the graph looks like as well would be beneficial to my understanding):
g(x)=3sin1/2(x+2)-1
This is exactly how the function is written, barring the fact that the 2 is directly under the 1 (so the (x+2) isn't under the fraction)
Thank you very much for your help!
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Find the amplitude and period for this function:
g(x)=3sin1/2(x+2)-1
the general formula is
y = g(x) = A sin (Bx+c) +k
now rewrite our equation into this form
g(x) = 3*sin(x/2 +1) -1
so A=3, B=1/2, C=1 and k=-1
Amplitude is |A| = |3| = 3 (this is the maimum deviation from the x axis)
period is 2pi/B = 2pi/1/2 = 4pi
k=-1 means that the graph is translated vertically down 1 unit
note that there is a phase shift defined as -C/B = -1/(1/2) = -2
the graph of g(x) completes one full cycle as x varies from -2, -2+4pi
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