Answer: f(x) = 6*sin( (1/8)*π*x) + 3
Step-by-step explanation:
A sine function is written as:
f(x) = A*sin(w*x + f) + M
where:
A = amplitude
w = frequency
f = phase
M = midline
Here we know that:
Frequency = 1/8π, then: w = (1/8)*π
Amplitde = 6, then A = 6
midline = 3, then M = 3
So our equation is:
f(x) = 6*sin( (1/8)*π*x + f) + 3.
Now we also know that:
y-inercept: (0,3)
This means that:
f(0) = 3 = 6*sin( (1/8)*π*0 + f) + 3 = 6*sin(f) + 3
Now we can remember that sin(0) = 0
Then we must have f = 0.
This means that the equation is:
f(x) = 6*sin( (1/8)*π*x) + 3
So the image of the function is:
