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 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`.

Answer 2

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.