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Identify the maximum and minimum values of the function y = 10 cos x in the interval [-2π ,2π]. Use your understanding of transformations, not your graphing calculator. (3 points)

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sqdancefan
The period of the cosine function is 2π, so the interval represents two full periods of the function. Within a period, the maximum is 1 and the minimum is -1.

The given function scales the cosine function vertically by a facor of 10. This tells you the transformed function will have a ...
  maximum of 10×(1) = 10
  minimum of 10×(-1) = -10
on the given interval.
frika
The range of the function [tex]y=\cos x[/tex] is [tex][-1,1][/tex] (in other words [tex]-1\le \cos x\le 1[/tex]). Then [tex]-10\le 10\cos x\le 10[/tex] that means that the range of the function [tex]y=10\cos x[/tex] is [tex]y\in [-10,10][/tex].

The minimal value is when 
[tex]y=-10, \\ 10\cos x =-10, \\ \cos x=-1, \\ x=\pi[/tex].

The maximal value is when
 [tex]y=10, \\ 10\cos x =10, \\ \cos x=1, \\ x=0[/tex].

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