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C) g(x) = 3^(x - 4) + 2

Step-by-step explanation:

Notice that function f(x) contains point (0, 1).

In function g(x), point (0, 1) of f(x) has been translated to point (4, 3).

A translation from point (0, 1) to point (4, 3) is a translation of 4 units in x and 2 units in y.

For function y = f(x) in general, if you replace x with x - h and y with y - k, that means a horizontal translation of h units and a vertical translation of k units.

From here we see we have h = 4 and k = 2.

x in f(x) must be replaced with x - 4.

y in f(x) must be replaced with y - 2.

y = f(x)

y - 2 = f(x - 4)

y = f(x - 4) + 2

f(x) = 3^x

g(x) = 3^(x - 4) + 2

C) 3^(x - 4) + 2

1/2(2*4)=6 $$- agahajakanajak