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

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

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:

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