Question

How do I describe in mathematical terms how the change in amplitude in the function effects the graph?

Answer 1

In general, a sine function has the form shown below

`\begin{gathered} y=Asin(Bx+C)+D \\ A\rightarrow\text{ amplitude} \\ B\rightarrow\text{ constant related to the period of the function} \\ C\rightarrow\text{ phase shift} \\ D\rightarrow\text{ vertical shift} \end{gathered}`

Therefore, a change in amplitude can be understood as multiplying the sine function by a constant, a vertical stretch. (Notice that A does not multiply D in the expression above)