Question

1) what is the phase shift of f(x) = -2sin(3x-pi)+1
2) What is the period of f(x) = -2sin(3x-pi)+1

Answer 1

3x-π = 3(x - π/3)
so the shift is π/3 to the right

the period of sin(kx) is 2π/k

Answer 2

In relation to what function?
f(x) = -2sin(3x-pi)+1 = f(x) = -2 sin (3(x-π/3) ) + 1 <---- a more standard form

if you are comparing f(x) = -2sin(3x-pi)+1 with f(x) = -2sin(3x)
you would have translated f(x) = -2sin(3x) one unit up and π/3 to the right

for the period, if y = a sin kx, the period is 2π/k units
so for yours .....