Question

4. Determine the appropriate algebraic model for the graphs below. Note: there is more than one possible answer.

Answer 1

For graph A,

Using the sine to model the graph

The formula to obtain the model is,

`y=Asin\left(Bx\right)`

where,

`\begin{gathered} A=Amplitude \\ B=(2\pi)/(Period) \end{gathered}`

Therefore,

`\begin{gathered} A=0.75=(3)/(4) \\ B=(2\pi)/(\pi)=2 \end{gathered}`

Hence, the model is

`y=(3)/(4)sin\left(2x\right)`

For graph B

Using the cosine to model the graph

The formula to obtain the model is,

`y=Acos\left(Bx\right)`

Therefore,

`\begin{gathered} A=-2 \\ Period=8\pi,\text{ }\therefore B=(2\pi)/(8\pi)=(1)/(4) \end{gathered}`

Hence, the model is

`y=-2cos\left((1)/(4)x\right)`