Question

Anybody know the right answer?

Answer 1

If we just have

`y = \cos x`

that's an amplitude of 1 and a period of
`2\pi`

Let's modify this step by step.

Amplitude of 4. Four times the amplitude means a factor of 4 on the outside.

`y = 4 \cos x`

Period of π. Double the period means a factor of 2 on the inside.

`y = 4 \cos(2x)`

Horizontal shift of π/2 to the left. To the left means adding a positive number to x. The question appear ambiguous. It's not clear to me if we add to x or 2x; let's make it

`y = 4 \cos(2(x + \frac \pi 2))`

Vertical shift of 3:

`y = 3 + 4 \cos(2(x + \frac \pi 2))`

`y = 3 + 4 \cos(2x + \pi)`

Depending on the interpretation of the phase shift, that pi may be a pi/2.

Answer:
`3 + 4 \cos(2x + \pi)`