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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].

For the function fx 3sinx 2 the distance between the maximum and minimum values is 6 Which statement must be true about this function HINT Its not B A The ampli class=

Respuesta :

JeanaShupp

Answer: A. The amplitude is 3.

Step-by-step explanation:

Given function : [tex]f(x) = -3sin(x) + 2[/tex]

Period of a sine function is [tex]2\pi.[/tex]

Since [tex]-1\leq \sin x \leq 1[/tex]

[tex]\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[/tex]

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

Amplitude = 3 [coefficient of sin x]

Only option A. is correct.

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