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nobillionaireNobley

f(x) = √(x - 8)
g(x) = √(x + 4)

The graph of g is obtained by shifting the graph of f 12 units to the left.

Answer:

g(x) is obtained by shifting the graph of f(x) 12 units in the left.

Step-by-step explanation:

we are given the function f(x) and g(x) as:

\(f(x)=\sqrt{x-8}\) and \(g(x)=\sqrt{x+4}\) or we can also say that \(g(x)=f(x+12)\).

so any function g(x)=f(x+h) is formed by shifting the function either to the right or to the left of the graph depending on whether this 'h' is positive or negative.

if h>0 then the shift will be towards the left and if this h<0 then the shift will be towards the right by 'h' units.

here h=12>0

Hence, g(x) is obtained by shifting the graph of f(x) 12 units in the left.