Looking at the graph, we have a trigonometrical function. It can be a sine or cosine function.
Since it has the point (0, 0), we can use the sine function to model it.
Let's use the following equation to model it:
[tex]y=a\sin (bx+c)+d[/tex]
Where a is the amplitude, b is a horizontal compression factor, c is a horizontal shift and d is a vertical shift.
Looking at the graph, the amplitude goes from -3.33 to 3.33, therefore the value of a is 3.33.
The period of the function is equal to pi (3.14). We can use the following formula for the period, so we can calculate the value of b:
[tex]\begin{gathered} T=\frac{2\pi}{b} \\ \pi=\frac{2\pi}{b} \\ b=2 \end{gathered}[/tex]
There is no horizontal or vertical shift, therefore c = 0 and d = 0.
So the function that represents this graph is:
[tex]y=3.33\sin (2x)[/tex]
Domain: All real numbers.
Range: [-3.33, 3.33].
Period: pi
