Question

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)

Answer 1

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.

Answer 2

The range of the function $y=\cos x$ is $[-1,1]$ (in other words $-1\le \cos x\le 1$). Then $-10\le 10\cos x\le 10$ that means that the range of the function $y=10\cos x$ is $y\in [-10,10]$.

The minimal value is when 
$y=-10, \\ 10\cos x =-10, \\ \cos x=-1, \\ x=\pi$.

The maximal value is when
 $y=10, \\ 10\cos x =10, \\ \cos x=1, \\ x=0$.