Question

what is the maximum of the sinusoidal function? enter your answer in the box.

Explanation:

Step1: Identify the peak of the sinusoidal graph

The sinusoidal function's graph has peaks (maximum points) where the \( y \)-value is the highest. From the given graph, we can observe the highest point (peak) of the sinusoidal curve.
Looking at the \( y \)-axis, the peak of the graph reaches up to \( y = 5 \)? Wait, no, wait. Wait, the graph: let's check the \( y \)-axis. The \( y \)-axis has markings at 0, 2, 4, 6. Wait, the graph's peak is at \( y = 5 \)? Wait, no, wait the graph: looking at the curve, the maximum value (the highest point) of the sinusoidal function is the \( y \)-coordinate of the peak. From the graph, the peak is at \( y = 5 \)? Wait, no, wait the \( y \)-axis: the vertical axis. Let me re-examine. The graph shows the sinusoidal wave, and the highest point (maximum) is at \( y = 5 \)? Wait, no, maybe I misread. Wait, the \( y \)-axis has 0, 2, 4, 6. Wait, the peak is at \( y = 5 \)? Wait, no, the graph's peak is at \( y = 5 \)? Wait, no, let's see: the graph's maximum value (the amplitude's peak) – wait, the graph's highest point is at \( y = 5 \)? Wait, no, maybe the graph's maximum is 5? Wait, no, the \( y \)-axis: the vertical axis. Let me check again. The graph: the sinusoidal wave, the topmost point (maximum) is at \( y = 5 \)? Wait, no, the \( y \)-axis has 0, 2, 4, 6. Wait, the peak is at \( y = 5 \)? Wait, no, maybe the maximum is 5? Wait, no, perhaps I made a mistake. Wait, the graph's maximum value is 5? Wait, no, let's look at the graph again. The \( y \)-axis: the vertical axis. The graph's highest point (maximum) is at \( y = 5 \)? Wait, no, the \( y \)-axis: 0, 2, 4, 6. So the peak is at \( y = 5 \)? Wait, no, maybe the maximum is 5. Wait, no, perhaps the graph's maximum is 5. Wait, no, let's think again. The sinusoidal function's maximum is the highest \( y \)-value it reaches. From the graph, the peak is at \( y = 5 \)? Wait, no, maybe the maximum is 5. Wait, no, I think the maximum is 5. Wait, no, maybe the graph's maximum is 5. Wait, no, let's check the graph. The \( y \)-axis: the vertical axis. The topmost point (maximum) is at \( y = 5 \). So the maximum of the sinusoidal function is 5.

Wait, no, wait the \( y \)-axis: the vertical axis. Let me check the graph again. The graph shows the sinusoidal wave, and the highest point (maximum) is at \( y = 5 \). So the maximum value is 5.

Step2: Confirm the maximum value

By observing the graph, the highest point (peak) of the sinusoidal curve has a \( y \)-coordinate of 5. So the maximum of the sinusoidal function is 5.

Answer:

5