Question

Find the domain and range for the graph and tell if it is a function or not

Answer 1

`\begin{gathered} D\colon\lbrace(-4,-1)\cup\lbrack-1,3)\cup\lbrack3,5\rbrack\rbrace \\ R\colon\mleft\lbrace-2,1,3\mright\rbrace \\ YES \end{gathered}`

Step-by-step explanation

We want to identify the domain, range, and if it is a function or not.

The domain is the set of all input values of the graph i.e. the set of all values of x that are on the graph.

From the graph, we have that the domain is:

`\mleft\lbrace(-4,-1)\cup\lbrack-1,3)\cup\lbrack3,5\rbrack\mright\rbrace`

The range of the graph is the set of all output values of the graph, i.e. the set of all values of y that are on the graph.

From the graph, we have that the range is:

`\mleft\lbrace-2,1,3\mright\rbrace`

A function is a relation whereby each value of x is mapped directly to only one value of y. In other words, every single value of x results in only one value of y.

From the graph, we see that it is a function.