IDENTIFYING FUNCTIONS FROM GRAPHS

For many functions we can obtain graphs. But,  not every graph will represent a function. Following test will help us to determining, whether the given graph is a function or not.

Vertical Line Test

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.

Example 1 :

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

Solution :

The given graph does not represent a function as a vertical line cuts the graph at two points P and Q.

Example 2 :

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

Solution :

The given graph represents a function as any vertical line will intersect the graph at most one point P.

Example 3 :

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

Solution :

The given graph does not represent a function as a vertical line cuts the graph at two points A and B.

Example 4 :

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

Solution :

The given graph represents a function as the graph satisfies the vertical line test.

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