To understand the function f(x) = 2sin(x) + 3, we need to analyze its components:
- 2sin(x): This part of the function oscillates between -2 and +2 because the sine function fluctuates between -1 and +1. When we multiply by 2, the range becomes from -2 to +2.
- +3: This shifts the entire graph of the sine function upwards by 3 units.
Therefore, the overall range of f(x) becomes from 1 to 5, since the minimum value of 2sin(x) + 3 is 1 (at sin(x) = -1) and the maximum value is 5 (at sin(x) = 1).
In summary, the function f(x) = 2sin(x) + 3 is periodic with a range of [1, 5].