Question

determine the amplitude of the following graph.

Explanation:

Step1: Recall the formula for amplitude

The amplitude of a sinusoidal function \(y = A\sin(Bx - C)+D\) or \(y = A\cos(Bx - C)+D\) is given by \(|A|\). It represents the maximum distance from the mid - line (average of the maximum and minimum values of the function) to the peak (or trough) of the graph.

Step2: Identify the maximum and minimum values from the graph

From the graph, the maximum value of the function \(y_{max}=3\) and the minimum value \(y_{min}=- 3\).

Step3: Calculate the amplitude

The formula for amplitude \(A=\frac{y_{max}-y_{min}}{2}\). Substitute \(y_{max} = 3\) and \(y_{min}=-3\) into the formula: \(A=\frac{3-(-3)}{2}=\frac{3 + 3}{2}=\frac{6}{2}=3\). Another way is to note that the distance from the mid - line (since \(y = 0\) is the mid - line for this graph as \(\frac{3+( - 3)}{2}=0\)) to the peak (where \(y = 3\)) is \(|3-0| = 3\).

Answer:

$3$