Question

determine the amplitude of the following graph.

Explanation:

Step1: Identify max and min values

From the graph, the maximum value (peak) is 5 and the minimum value (trough) is 1? Wait, no, wait. Wait, looking at the y - axis, the peaks seem to be at y = 5? Wait, no, the grid: let's check the y - coordinates. Wait, the graph has a peak and a trough. Wait, maybe I misread. Wait, the amplitude is calculated as $\frac{\text{Max Value}-\text{Min Value}}{2}$. Let's find the max and min. Looking at the graph, the highest point (maximum) is 5? Wait, no, the y - axis has marks: 5, 3, 2, 1, - 1, - 2, - 3, - 4, - 5. Wait, maybe the maximum value (the height of the peak) and the minimum value (the depth of the trough). Wait, let's see: the graph oscillates. Let's take two points: the maximum y - value (let's say) is 5? No, wait, the y - axis at x = 0, the graph crosses y = 4? Wait, maybe I made a mistake. Wait, let's re - examine. The formula for amplitude of a periodic function (like a sine or cosine wave) is $A=\frac{\text{Max}-\text{Min}}{2}$. Let's find the maximum and minimum y - values. From the graph, the highest point (peak) is at y = 5? Wait, no, the grid lines: the y - axis has a mark at 5, 3, 2, 1, 0, - 1, - 2, - 3, - 4, - 5. Wait, maybe the maximum value is 5 and the minimum value is 1? No, that can't be. Wait, maybe the midline is at y = 3? Wait, let's see: the distance from the midline to the peak is the amplitude. Let's find the midline. The midline is the average of the maximum and minimum values. Let's look for the highest and lowest points. Suppose the maximum value (peak) is 5 and the minimum value (trough) is 1. Then the midline is $\frac{5 + 1}{2}=3$. Then the amplitude is the distance from midline to peak: $5-3 = 2$. Wait, let's check: if midline is 3, peak is 5 (3 + 2), trough is 1 (3 - 2). Yes, that makes sense. So Max = 5, Min = 1. Then amplitude $A=\frac{5 - 1}{2}=\frac{4}{2}=2$.

Step2: Calculate amplitude

Using the formula for amplitude $A=\frac{\text{Max}-\text{Min}}{2}$. Let Max = 5 and Min = 1. Then $A=\frac{5 - 1}{2}=\frac{4}{2}=2$.

Answer:

2