Question

the graph of a trigonometric function is shown. what is the amplitude of this function?

Explanation:

Step1: Recall the formula for amplitude

Amplitude \(A=\frac{\text{Maximum value}-\text{Minimum value}}{2}\)

Step2: Identify maximum and minimum values

From the graph, the maximum value \(y_{max} = 3\) and the minimum value \(y_{min}=-1\)

Step3: Calculate the amplitude

Substitute into the formula: \(A=\frac{3 - (-1)}{2}=\frac{3 + 1}{2}=\frac{4}{2}=2\)

Answer:

\(2\)