Answer:
(b) f(x)=9sin(6πx)+3
Step-by-step explanation:
The answer choices differ in the vertical offset and in the frequency.
For frequency f, the argument of the sine function needs to be 2πfx. Here, the frequency of 3 means the argument of the sine function is 2π·3x = 6πx.
The sine function is 0 when x=0, so the y-intercept is the vertical offset: 3.
The only reasonable choice is ...
f(x) = 9·sin(6πx) +3
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Additional comment
The function a·sin(bx) +c has amplitude 'a', frequency b/(2π), and vertical offset 'c'. The amplitude is half the difference between the maximum and the minimum: a=(12 -(-6))/2 = 9. For x=0, the y-intercept is the vertical offset (midline of the function), 'c'.
