A certain cosine function completes 6 cycles over the interval [0,2π].
Which function rule could model this situation?
f(x)=cos(16x)
f(x)=cos(x)+6
f(x)=cos(6x)
f(x)=6cos(x)
see above
What type of answer is that?
f(x)=cos(6x)
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To determine the correct function rule, we need to analyze how the number of cycles relates to the coefficients and arguments of the cosine function.
The general form of a cosine function is f(x) = A*cos(Bx), where A represents the amplitude and B represents the frequency (or number of cycles).
In this case, we know that the cosine function completes 6 cycles over the interval [0,2π]. Since the interval [0,2π] corresponds to one full revolution or 2π radians, we can conclude that the function completes 6 cycles within 2π radians.
To find the frequency, we need to divide the total number of cycles by the length of the interval. In this case, it would be 6 cycles / 2π radians. Simplifying the expression, we get 3/π.
Therefore, the correct function rule that models this situation is f(x) = cos((3/π)x), which represents a cosine function that completes 6 cycles over the interval [0,2π].
Among the options provided, f(x) = cos(6x) is the correct function rule that matches the given situation.