Functions are used to represent graphs, and vice versa.
The function represented by the graph is 
The graph (see attachment) is an absolute value graph.
An absolute value graph is represented as:

Where

The vertex is the minimum or the maximum point on the graph.
So, we have:

The function becomes

The function also passes through the point (-1,0).
So, we have:


Remove the absolute bracket

Subtract 3 from both sides

Divide both sides by 3

Substitute -1 for (a) in 

Hence, the function represented by the graph is 
Read more about absolute value graphs at:
brainly.com/question/3381225