If we just have
[tex]y = \cos x[/tex]
that's an amplitude of 1 and a period of [tex]2\pi[/tex]
Let's modify this step by step.
Amplitude of 4. Four times the amplitude means a factor of 4 on the outside.
[tex]y = 4 \cos x[/tex]
Period of π. Double the period means a factor of 2 on the inside.
[tex]y = 4 \cos(2x)[/tex]
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
[tex]y = 4 \cos(2(x + \frac \pi 2))[/tex]
Vertical shift of 3:
[tex]y = 3 + 4 \cos(2(x + \frac \pi 2))[/tex]
[tex]y = 3 + 4 \cos(2x + \pi)[/tex]
Depending on the interpretation of the phase shift, that pi may be a pi/2.
Answer: [tex]3 + 4 \cos(2x + \pi)[/tex]
