Identify the maximum and minimum values of the function in the interval $ [-2 \pi, 2 \pi] $. Use your understanding of transformations, not your graphing calculator.
-$$y = - \frac { 1 } { 2 } \cos x$$
A) Maximum value $= \frac { 1 } { 2 } ;$ minimum value $= - \frac { 1 } { 2 }$
B) Maximum value $= \frac { 1 } { 4 } ;$ minimum value $= 0$
C) Maximum value $= \frac { 1 } { 4 } ;$ minimum value $= - \frac { 1 } { 4 }$
D) Maximum value $= \frac { 1 } { 2 } ;$ minimum value $= 0$

Question

Quizplus · Accepted Answer

The original cosine function has a maximum value of 1 and a minimum value of -1. Multiplying by -1/2 flips the graph and scales the values, making the new maximum $ \frac{1}{2} $ and the new minimum $ -\frac{1}{2} $.

Identify the Maximum and Minimum Values of the Function in the Interval