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 = - 9 \sin x$
A) Maximum value $= 18$; minimum value $= - 18$
B) Maximum value $= 9$; minimum value $= 0$
C) Maximum value $= 9$; minimum value $= - 9$
D) Maximum value $= 18$; minimum value $= 0$

Question

Quizplus · Accepted Answer

The function $y = -9 \sin x$ is a vertical stretch of the basic sine function by a factor of 9, with a reflection across the x-axis due to the negative sign. The sine function has a maximum value of 1 and a minimum value of -1. Multiplying these by -9 gives a maximum value of $9$ (since $-9 \times -1 = 9$) and a minimum value of $-9$ (since $-9 \times 1 = -9$).

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