I had to create a function that had to satisfy all these criterias:

Here is the function I came up with: f(x) = 10sin (12/11x + 5.5) +15

Phase shift = 5.5 x 11/12 = roughly 5

period = 11pi/6

next I had to follow this:

"Using that function you created, model after a real-life application and create a word problem. Then use the function to solve the problem. Examples of real-life application include tide, ferris wheel, weight on a spring, etc."

Here is the question I've created:

Lina and Adam are on a ferris wheel at the local fair. The Ferris wheel has a diameter of 20 meters and takes 15 minutes to complete one full revolution. The lowest point of the Ferris wheel is 5 feet above the ground, and it reaches its highest point at 25 meters above the ground. When they start their ride, Emma notices that the ride operator started the Ferris wheel with the bottom seat at the lowest point. Liam wonders how high above the ground they will be after 8 minutes into the ride.

How would I tweak the numbers in the question to match up with the function so that if you were to solve for f(8) (8 minutes), the answer matches more or less with a graph, should be (8, 14.144).

Make sure that every piece of information from the formula is unexplicitly stated in the question, so that one could piece together the entire function 10sin(12/11x +5.5)+15 from the question itself one way or another. Ex, the diameter is 20m. Therefore someone could induce that the amplitude is 10. Make sure to add information that would allow for the person to find the phase shift to be 5.5, period to be 12/11, amplitude to be 10, and vertical shift to be 15

- Amplitude greater than 5 - Midline value greater than 5 - Max greater than 20 - Minimum lower than 10 - A non-zero phase shift - Period of either 34 or 611