Answer:
[-1, 7]
Explanation:
If you mean ...
y = 4sin(2x) +3
then you can substitute the range of the sine function into the equation and evaluate it to find the range of y.
The range of sin( ) is [-1, 1], so the range of y is ...
4[-1, 1] +3 = [4(-1)+3, 4(1)+3] = [-1, 7]
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Comment on the problem statement
The range of y = 4sin²(x)+3 will be different, and the range of 4sin(2x+3) will be different yet. It is usually a good idea to use parentheses around function arguments.