The sinusoidal function described is f(x) = 4*cos(x/2) + 2.
What is the equation of the function described?
First, the amplitude is equal to half of the difference between the maximum and the minimum, so the amplitude is:
A = (6 - (-2))/2 = 4
The midline is equal to the minimum plus the amplitude:
M = -2 + 4 = 2.
now, we know that the y-intercept (when the function is evaluated in x = 0) is 6, so from that we conclude that we have a cosine function:
f(x) = 4*cos(kx) + 2
Notice that when evaluated in zero, we get:
f(0) = 4*cos(0) + 2 = 6.
Finally, we need to find the value of k.
Notice that the period of this function is 4π, while the period of the general cosine function is 2π, then we must have:
k*4π = 2π
Solving for k, we get:
h = (2π)/(4π) = 1/2.
Then the sinusoidal function described is f(x) = 4*cos(x/2) + 2.
If you want to learn more about sinusoidal functions:
https://brainly.com/question/9565966
#SPJ1
