Question

what is the amplitude of the function below?
options: 1, 2, π, 2π

Explanation:

Step1: Recall Amplitude Definition

Amplitude of a sinusoidal function is the maximum distance from the midline (average of maximum and minimum values) to a peak (or trough). Mathematically, amplitude \( A=\frac{\text{Max}-\text{Min}}{2} \).

Step2: Identify Max and Min Values

From the graph, the maximum \( y \)-value (peak) is \( 2 \), and the minimum \( y \)-value (trough) is \( -2 \)? Wait, no—wait, looking again: Wait, the peak is at \( y = 2 \)? Wait no, the graph: let's check the grid. The peak is at \( y = 2 \)? Wait, no, the first peak is at \( y = 2 \)? Wait, no, the y-axis has marks at 2, -2. Wait, the maximum value (highest point) is \( 2 \), minimum (lowest point) is \( -2 \)? Wait, no, wait the graph: the first peak is at y=2, then trough at y=-2? Wait, no, let's recalculate. Wait, the formula is \( A=\frac{\text{Max}-\text{Min}}{2} \). Let's find Max and Min. From the graph, the highest point (maximum) is \( 2 \), the lowest point (minimum) is \( -2 \)? Wait, no, wait the y-axis: the top grid line is 4, then 3, 2, 1, 0, -1, -2, -3, -4. The peak is at y=2, trough at y=-2. So Max = 2, Min = -2. Then \( A=\frac{2 - (-2)}{2}=\frac{4}{2}=2 \). Wait, or maybe I misread. Wait, another way: amplitude is the distance from midline to peak. The midline here: what's the average of max and min? If max is 2, min is -2, midline is 0. Then distance from midline (0) to peak (2) is 2. So amplitude is 2.

Answer:

2