# What could be the Function Graphed Below?

## An Introduction to Graphing Functions

At first glance, it may be difficult to identify what type of function is being graphed. Fortunately, by understanding the basics of graphing functions, you can determine which type of function is displayed. A function is a mathematical relationship between two variables, usually expressed as an equation. Graphing functions involves plotting their points on a coordinate plane and then connecting the points in order to create a graph.

## Examining the Graph

The graph below displays a function, but it’s not easy to determine which type of function it is. To identify the type of function, you must examine the characteristics of the graph. Start by looking at the endpoints, or the points at the beginning and end of the graph. If the endpoints are the same, the graph is a circle, which is not a function. If the endpoints are different, the graph may be a linear, quadratic, or exponential function.

## Identifying a Linear Function

The graph below appears to have different endpoints, so it could be a linear function. To identify a linear function, first look at the rate of change. A linear function has a constant rate of change, which means the same amount is added or subtracted from the y-coordinate each time the x-coordinate increases by one. You can determine this by looking at the change in the y-coordinate between two points on the graph. In the graph below, the rate of change is consistent, so it is likely a linear function.

## Identifying a Quadratic or Exponential Function

It is more difficult to determine whether the graph represents a quadratic or exponential function. To identify a quadratic function, look for a parabola shape, which is a symmetrical curved line. To identify an exponential function, look for a curve that is curved in one direction, usually from the bottom left to the top right. If the graph does not have either of these characteristics, then it is likely a linear function.

## Conclusion

By examining the characteristics of the graph, you can determine which type of function is being graphed. In the graph below, the endpoints are different and the rate of change is constant, so it is likely a linear function. You can also identify quadratic and exponential functions by looking for a parabola or curved line shape.