-How does changing the function from f(x) = 3 sin 2x to g(x) = 3 sin 2x + 5 affect the range of the function?

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 3 units, so the range changes from −3 to 3 in f(x) to 0 to 6 in g(x).

The function shifts up 5 units, so the range changes from −1 to 1 in f(x) to 4 to 6 in g(x).

The function shifts up 5 units, so the range changes from −3 to 3 in f(x) to 2 to 8 in g(x).

Question

-How does changing the function from f(x) = 3 sin 2x to g(x) = 3 sin 2x + 5 affect the range of the function?

 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 3 units, so the range changes from −3 to 3 in f(x) to 0 to 6 in g(x).

 The function shifts up 5 units, so the range changes from −1 to 1 in f(x) to 4 to 6 in g(x).

 The function shifts up 5 units, so the range changes from −3 to 3 in f(x) to 2 to 8 in g(x).

anonymous · Answer

what is the range of sin 2x ?

anonymous · Answer

$$\left| \sin 2x \right|\le 1$$
$$-1\le \sin 2x \le 1$$
multiply by 3,
what do you get?

anonymous · Answer

are you on the line ?

anonymous · Answer

$$-3\le 3\sin 2x \le 3$$
add 5 to each and get the result.