Answer:
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
Answer: C) 3^(x - 4) + 2
