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

1 Answer
Jan 4, 2017

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