Answer:
y = 4cos((π/5)x) +3
Step-by-step explanation:
The graph shows the peak of the function to be at x=0, so a cosine function is an appropriate choice for the model.
The value of A is half the difference between the minimum and maximum, so is ...
A = (1/2)(7 -(-1)) = 4
The value of C is the average of the maximum and the minimum, so is ...
C = (1/2)(7 +(-1)) = 3
The value of k must be chosen so that for one full period, kx is 2π. We note that one minimum is at -5, and the next is at +5, so the period of this waveform is (5 -(-5)) = 10. Then ...
k·10 = 2π
k = π/5 . . . . . divide by 10 and reduce the fraction
Now, we have all the parameters of our function:
y = 4cos((π/5)x) +3
