Question

question 10 next 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 \(|A|\). Geometrically, the amplitude is the distance from the mid - line of the graph to the maximum (or minimum) value of the function.

Step2: Identify the mid - line and maximum/minimum values

The mid - line of the given graph is \(y = 0\) (since the graph is symmetric about the \(x\) - axis). The maximum value of the function (the highest \(y\) - value) is \(y = 1\) and the minimum value is \(y=-1\).

Step3: Calculate the amplitude

Using the formula for amplitude (distance from mid - line to maximum/minimum), \(A=\vert y_{\text{max}}-y_{\text{mid}}\vert\). Here, \(y_{\text{max}} = 1\) and \(y_{\text{mid}}=0\), so \(A=\vert1 - 0\vert=1\) (or using \(y_{\text{min}}=-1\), \(A=\vert- 1-0\vert = 1\))

Answer:

$1$