The graph of f (x) = 1/x^2 is vertically compressed by a factor of 1/2 units, then shifted to the left 5 units and down 4 units.

G (x) =

G (x) = (1/2) (1 / (x + 5) ^2 - 4

Step-by-step explanation:

G (x) = bf (x - h) + k

represents the function f (x) shifted right h units, up k units and scaled vertically by a factor of b. Your problem statement tells you ...

f (x) = 1/x^2, b = 1/2, h = - 5, k = - 4

so your G (x) is ...

G (x) = (1/2) (1 / (x + 5) ^2 - 4