Answer: The equation that matches the function shown in the graph is y = 2 sin(x) + 1.
To understand why this is the correct equation, let's break it down step by step:
1. The graph shows a sinusoidal function, which means it resembles the shape of a sine wave.
2. The general form of a sinusoidal function is y = A sin(Bx + C) + D, where A, B, C, and D are constants that determine the characteristics of the graph.
3. In the given equation, y = 2 sin(x) + 1, A is 2, which means the amplitude of the graph is 2. This tells us that the graph oscillates between a maximum value of 2 and a minimum value of 0.
4. The term sin(x) represents the period of the graph. Since there is no coefficient in front of x, B is equal to 1, which means the period is the standard 2π.
5. The constant term 1, represented by D, shifts the entire graph vertically upwards by 1 unit.
6. By comparing the equation y = 2 sin(x) + 1 with the options provided, we can see that it matches with option D.
In summary, the equation y = 2 sin(x) + 1 matches the function shown in the graph because it has the correct amplitude, period, and vertical shift.
Have a good day :)
