Question

1. Identify all the key features of the following graph

Answer 1

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:

`y=a\sin (bx+c)+d`

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:

`\begin{gathered} T=(2\pi)/(b) \\ \pi=(2\pi)/(b) \\ b=2 \end{gathered}`

There is no horizontal or vertical shift, therefore c = 0 and d = 0.

So the function that represents this graph is:

`y=3.33\sin (2x)`

Domain: All real numbers.

Range: [-3.33, 3.33].

Period: pi