write a function with the following properties

Question

1. Write a function with the following properties: The type of function of f is cosine.
2. The amplitude of f is 1.
3. The period of f is 1π.
4. The phase shift of f is (3/8)π to the left.
5. The vertical shift of f is 5 up.

The function is f(x)= 

Answer 1

Hello Alison,

You use the general formula f(x) = Acos(B (x - C) ) + D and apply it to this specific problem.

A represents the amplitude so A = 1

B = 2π/period; period = 1 π so B = 2π/(1π) = 2

C represents the phase shift so C = -3π/8 because it’s to the left

D represents the vertical shift, so D = 5 because “5 up” means you ADD 5.

Plug A, B, C and D in the general formula and you get:

f(x) = 1cos(2(x - -3π/8) ) + 5

you can remove the 1 in front of cos because multiplying anything by 1 doesn’t change the result:

f(x) = cos(2(x + 3π/8) ) + 5

That is already correct as it is, but you can expand the part in bold if you'd like, and you get:

f(x) = cos(2x + 3π/4) + 5