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.

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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