identify a graph with a given amplitude\nwhich graph has an amplitude of $\frac{1}{2}$?

Explanation:

Step1: Recall amplitude definition

The amplitude of a periodic - function (like a sine or cosine wave) is the distance from the mid - line to the maximum or minimum value of the function.

Step2: Analyze first graph

In the first graph, the maximum value above the mid - line ($y = 0$) is 1 and the minimum value below the mid - line is - 1. So the amplitude $A=1$.

Step3: Analyze second graph

In the second graph, the maximum value above the mid - line ($y = 0$) is 2 and the minimum value below the mid - line is - 2. So the amplitude $A = 2$.

Step4: Analyze third graph

In the third graph, the maximum value above the mid - line ($y = 0$) is $\frac{1}{2}$ and the minimum value below the mid - line is $-\frac{1}{2}$. So the amplitude $A=\frac{1}{2}$.

Answer:

The third graph has an amplitude of $\frac{1}{2}$.