Question

A sine function has the following key features:

Answer 1

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: