Question

determine the amplitude of the following graph. answer submit answer

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 \(|A|\). Geometrically, the amplitude is the distance from the mid - line of the graph to the maximum (or minimum) value of the function.

Step2: Find the mid - line and maximum value

From the graph, we can observe that the mid - line \(y = 0\) (since the graph is symmetric about the \(x\) - axis in terms of vertical displacement). The maximum value of the function \(y_{max}=2\).

Step3: Calculate the amplitude

Using the formula for amplitude (distance from mid - line to maximum), \(A=\vert y_{max}-y_{mid - line}\vert\). Substituting \(y_{max} = 2\) and \(y_{mid - line}=0\), we get \(A = 2\).

Answer:

$2$