Question

There numbers on the side go from 1 1.5 2 2.5 3 sorry that there hard to readDetermine the sinusoids function for the graph

Answer 1

To start with, we will first have to define some terms:

Period: This is the time taken to complete one oscillation.

From the graph, we can observe that 1 oscillation was completed in 1 second,

Thus, the period (T) =1

`T=1`

we will use the formula below to get the sinusoidal function

`\begin{gathered} y=A\sin (Bx+C)+D \\ \text{where} \\ B=(2\pi)/(T)=(2\pi)/(1)=2\pi \\ C=Phase\text{ shift}=0 \\ D=Vertical\text{ shift}=2 \\ A=\text{amplitude}=1 \end{gathered}`

We can then substitute these values into the equation to derive the function

`\begin{gathered} y=1\sin (2\pi(x)+0)+2 \\ y=\sin (2\pi x)+2 \end{gathered}`

The graph of the function is shown below

The graph of the parent function is the one in blue, the function is

`y=\sin (2\pi x)`

The required graph is that in red, to obtain the graph, there will be a vertical shift of 2 in the parent function. This function is:

`y=\sin (2\pi x)+2`

Thus the answer is:

`y=\sin (2\pi x)+2`