The parent function of f(x) is the absolute value function: g(x) = |x|.
From this function, the value of x was decreased by 3 units, so we have a horizontal translation of 3 units to the right.

Then, the value of the function was multiplied by the factor 1/2, which means a vertical shrunk by a factor of 2:
![g^(\prime)^^(\prime)(x)=(1)/(2)g^(\prime)(x)=(1)/(2)|x-3|]()
And finally, the value of the function increased by 1 unit, which means a vertical translation of 1 unit up:

Therefore the correct option is the second one.