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help with amplitude graphs

 
 
describe the following graphs of y.  give (a) its amplitude (if applicable), (b) its maximum and minimum (if applicable) and (c) its period.  List if it has no amplitude, maximum, or minimum.
 
 
a.  y = tan 2x
 
 
 
b.  y = 3 sin 1/3 x
 
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1 Answer

1) y=tan(2x)
a)  The tangent function does not have an amplitude since its range is ±∞
b)  The tangent's range is ±∞, so it has no maximum or minimum
c)  The 2 in the argument of the tangent cuts the period in half.  The period of tan(x) is pi, so the period of tan(2x) is pi/2.
 
2) y=3sin(x/3)
a) The amplitude of sin(x) is 1.  The amplitude of 3 sin(x) is 3
b) The range of 3sin(x/3) is ±3, so +3 is its maximum and -3 is its minimum.
c) the period of sin(x) is 2pi.  The 1/3 in the argument makes the sine function take 3 times longer to complete its period, so the period of 3sin(x/3) = (2pi)(3) = 6pi