SOLUTION: A sinusoidal function whose period is 12 , maximum value is 10, and minimum value is −4 has a y-intercept of 3. What is the equation of the function described?

Question 1128231: A sinusoidal function whose period is 12 , maximum value is 10, and minimum value is −4 has a y-intercept of 3.
What is the equation of the function described?

f(x)=7cos(4x)+3
f(x)=7cos(4πx)+3
f(x)=7sin(4πx)+3
f(x)=7sin(4x)+3
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

With a maximum of 10 and a minimum of -4, the center line is y=3 and the amplitude is 7. In all of the answer choices the "7" and "3" are in the right place.

The period of sin(kx) or cos(kx) is 2pi/k. With the given answer choices, the period is then either 2pi/4pi = 1/2 or 2pi/4 = pi/2.
A period of 12 is not possible with the given answer choices. Apparently the period is supposed to be 1/2 instead of 12.

It would be polite to make sure you have shown your question correctly before posting.....

So assuming the period is supposed to be 1/2, then the answer has to involve either sin((4pi)x) or cos((4pi)x). Since the y-intercept of 3 is the center line of the function, the function is a sine function.

ANSWER: f(x) = 7sin((4pi)x)+3
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SOLUTION: A sinusoidal function whose period is 12 , maximum value is 10, and minimum value is &#8722;4 has a y-intercept of 3. What is the equation of the function described?

SOLUTION: A sinusoidal function whose period is 12 , maximum value is 10, and minimum value is −4 has a y-intercept of 3. What is the equation of the function described?