Question

What cosine function represents a amplitude of 3, a period of `pi`, no horizontal shift, and a vertical shift of 2?

Answer 1

`f(x)=3cos(2x)+2`

Explanation:

We are able to use the transformation formula `f(x)=a*cos((x-h)/b)+k`. You start with `f(x)=cos(x)` and replace `a` with the desired amplitude, `h` with the desired horizontal shift, and `k` with the desired vertical shift. This leaves out the `b`-value. A regular cosine function has a period of `2pi`. If you want a period of `pi`, since that is one half of the original period, you need to replace your `b` with a `1/2`.
This is about how it would work out. `f(x)=3*cos((x-0)/(1/2))+2` From there you simplify your equation giving you `f(x)=3cos(2x)+2`