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How does changing the function from f(x) = 2 sin 4x to g(x) = 2 sin 4x + 3 affect the range of the function?
The function shifts up 3 units, so the range changes from −2 to 2 in f(x) to 1 to 5 in g(x). The function shifts up 3 units, so the range changes from −1 to 1 in f(x) to 2 to 4 in g(x). The function shifts up 4 units, so the range changes from −2 to 2 in f(x) to 2 to 6 in g(x). The function shifts up 4 units, so the range changes from −1 to 1 in f(x) to 3 to 5 in g(x).

Question

Please help! I'll fan and medal!
How does changing the function from f(x) = 2 sin 4x to g(x) = 2 sin 4x + 3 affect the range of the function? 
 The function shifts up 3 units, so the range changes from −2 to 2 in f(x) to 1 to 5 in g(x).  The function shifts up 3 units, so the range changes from −1 to 1 in f(x) to 2 to 4 in g(x).  The function shifts up 4 units, so the range changes from −2 to 2 in f(x) to 2 to 6 in g(x).  The function shifts up 4 units, so the range changes from −1 to 1 in f(x) to 3 to 5 in g(x).