Question

What is the domain of the function written as a compound inequality?

Answer 1

We are given a graph and asked to find the domain and the range of the graph in compound inequality form.

Domain:

The domain of a function is all the possible input (x) values for which the function is defined.

As you can see, the function is defined for x is equal to or greater than 2 and equal to or less than -4

So, the domain of the function is

`2\le x\le-4`

Range:

The range of a function is all the possible output (y) values corresponding to the input (x) values.

As you can see, the range of the function is y is equal to or greater than -4 and equal to or less than 5

`-4\le y\le5`

Therefore, the domain and range of the given function in the compound inequality form is

`\begin{gathered} domain\colon2\le x\le-4 \\ range\colon-4\le y\le5 \end{gathered}`