Question

For the function f(x) = -3sin(x) + 2, the distance between the maximum and minimum values is 6. Which statement must be true about this function? HINT: It's not B.

A. The amplitude is 3.
B. The midline is y = 3.
C. The period of the function is 3pi.
D. The range is [-3, 3].

Answer 1

Answer: A. The amplitude is 3.

Explanation:

Given function :
`f(x) = -3sin(x) + 2`

Period of a sine function is
`2\pi.`

Since
`-1\leq \sin x \leq 1`

`\Rightarrow\ -3\leq -3\sin x\leq 3\\\\\Rightarrow\ -3+2\leq -3\sin x+2\leq 3+2\\\\\Rightarrow\ -1\leq -3\sin x+2\leq 5`

i.e. Range is [-1,5]

Amplitude = 3 [coefficient of sin x]

Only option A. is correct.