# HOW TO IDENTIFY FUNCTION FROM GRAPH

## About the topic "How to identify function from graph"

How to identify function from graph ?

By using the concept vertical line test, we can easily check whether the graph represents the function or not.

This is a tool which can be used to test whether the given graph represents a function or not.

The following are the steps of vertical line test :

Step 1 :

Draw a vertical line at any where on the given graph.

Step 2 :

We have to check whether the vertical line drawn on the graph intersects the graph in at most one point.

Step 3 :

If the vertical line intersects the graph in at most one point, then the given graph represents a function.

If the vertical line intersects the graph in more than one point, then the given graph does not represent a function.

Caution :

For some graphs, the vertical line will intersect the graph in one point at one position and more than one point at a different position.

In the above situation, the graph will not represent a function.

Key concept :

A graph represents a function only if every vertical line intersects the graph in at most one point.

We can have better understanding on vertical line test for functions through the following examples.

Example 1 :

Use the vertical line test to determine whether the following graph represents a function.

Solution :

Step 1 :

Draw a vertical line at any where on the given graph.

Step 2 :

We have to check whether the vertical line drawn on the graph intersects the graph in at most one point.

Step 3 :

In the above graph, the vertical line intersects the graph in at most one point, then the given graph represents a function.

Example 2 :

Use the vertical line test to determine whether the following graph represents a function.

Solution :

Step 1 :

Draw a vertical line at any where on the given graph.

Step 2 :

We have to check whether the vertical line drawn on the graph intersects the graph in at most one point.

Step 3 :

In the above graph, the vertical line intersects the graph in more than one point (three points), then the given graph does not represent a function.

Example 3 :

Use the vertical line test to determine whether the following graph represents a function.

Solution :

Step 1 :

Draw a vertical line at any where on the given graph.

Step 2 :

We have to check whether the vertical line drawn on the graph intersects the graph in at most one point.

Step 3 :

In the above graph, the vertical line intersects the graph in more than one point (three points), then the given graph does not represent a function.

Example 4 :

Use the vertical line test to determine whether the following graph represents a function.

Solution :

Step 1 :

Draw a vertical line at any where on the given graph.

Step 2 :

We have to check whether the vertical line drawn on the graph intersects the graph in at most one point.

Step 3 :

In the above graph, the vertical line intersects the graph in at most one point, then the given graph represents a function.

Example 5 :

Use the vertical line test to determine whether the following graph represents a function.

Solution :

Step 1 :

Draw a vertical line at any where on the given graph.

Step 2 :

We have to check whether the vertical line drawn on the graph intersects the graph in at most one point.

Step 3 :

In the above graph, the vertical line intersects the graph in more than one point (three points), then the given graph does not represent a function.

After having gone through the stuff given above, we hope that the students would have understood "How to identify function from graph"

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