The parent function, f(x) = 5x, has been vertically compressed by a factor of one-half, shifted to the right three units and down two units.
choose the correct function to represent the transformation.

We are given the parent function, f(x) = 5x and is vertically compressed by a factor of 1/2, shifted to the right (3 units) and down two units. 

Vertical compression makes the function:

f(x) = (1/2) * 5x

shifted 3 units to the right makes the function:

f(x) = (1/2) * 5 (x+3)

shifted 2 units down makes the function:

f(x) = (1/2) *(5 (x+3)) - 2 

therefore, this function is the resulting function after performing all three adjustments of the parent function. First, compression, then shift to left/right, then shift up and down.