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,

$\begin{gathered} A=Amplitude \\ B=\frac{2\pi}{Period} \end{gathered}$

Therefore,

$\begin{gathered} A=0.75=\frac{3}{4} \\ B=\frac{2\pi}{\pi}=2 \end{gathered}$

Hence, the model is

$y=\frac{3}{4}sin\left(2x\right)$

For graph B

Using the cosine to model the graph

The formula to obtain the model is,

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

Therefore,

$\begin{gathered} A=-2 \\ Period=8\pi,\text{ }\therefore B=\frac{2\pi}{8\pi}=\frac{1}{4} \end{gathered}$

Hence, the model is

$y=-2cos\left(\frac{1}{4}x\right)$