Which of the following functions illustrates a change in amplitude?

To illustrate a change in amplitude, we need to first understand the term 'amplitude' in the context of a function. In the case of periodic functions, such as sine or cosine functions that model wave-like phenomena, the amplitude refers to the maximum extent of a vibration or oscillation, measured from the position of equilibrium. In mathematical terms, it's the distance from the middle value (the axis of the graph) to the peak or trough of the wave.

A basic sine function is written as f(x) = sin(x). To change its amplitude, you would multiply the function by a factor 'A', which represents the amplitude. A modified sine function with amplitude 'A' would be written as:

f(x) = A * sin(x)

If A is greater than 1, the amplitude of the wave is increased; if A is between 0 and 1, the amplitude is decreased. An example of a function that illustrates a change in amplitude is:

f(x) = 3 * sin(x)

Here, the amplitude has been changed from the standard sine function because the function has been multiplied by 3. This means the peaks and troughs of the wave will extend three times farther from the x-axis than they would in the basic sine function.