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).

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).

mathmale · Answer

Look carefully.  How are functions f(x) and g(x) different?

If you graphed the basic parabola y=x^2, and called that w(x), how would the graph of z(x)=x^2 + 3 differ from that of w(x)?