Question

A sine function has the following key features:

Frequency = 1/4π

Amplitude = 2

Midline: y = 2

y-intercept: (0, 2)

The function is not a reflection of its parent function over the x-axis.
Graph.

Answer 1

@dude

Answer 2

So for any sine function

asin(b(x+c))+d
is the general system for transformations.

-We are given that the amplitude, a, is 2. Hence, a=2.

-Now, we are given the frequency. If you may recall from Physics (or maybe even your math class it was covered), frequency is the inverse of period. \(f=\frac{1}{T}\)
Hence, if f=1/4π, then T=1/1/4π=4π
Using the period, we can solve for the value of b from our transformation.
Recall that \(T=\frac{2π}{b}\)
Plug T in and you'll get b=1/2.

-There is no phase shift noted in the given information, so we can simply ignore c.

-The midline is y=2, so we can assume d=2. This is true with our y-intercept, because if you plug in x=0, it would be 2sin(1/2(0)) + 2 which is just 2.

Hence you should have your sine function as

\(2sin(\frac{1}{2}x)+2\)

You can graph it on desmos or work backward just to be sure that you are correct. It's been a while since I've done these, so if someone else wants to check, then please do (:

Answer 3

Also, the last point holds true, because the parent function, y=sinx, is not obtained if you reflect the described function we found.