IDENTIFYING FUNCTIONS FROM MAPPING DIAGRAMS

A function assigns only output to each input. The value that is put into a function is the input. The result is the output.

A mapping diagram can be used to represent a relationship between input values and output values. A mapping diagram represents a function if each input value is paired with only one output value.

Example 1 :

Determine whether the relationship given in the mapping diagram is a function.

Solution :

Because each input value is paired with only one output value, the relationship given in the above mapping diagram is a function.

Example 2 :

Determine whether the relationship given in the mapping diagram is a function.

Solution :

Because 2 is paired with more than one output value (both 20 and 40), the relationship given in the above mapping diagram is not a function.

Example 3 :

Determine whether the relationship given in the mapping diagram is a function.

Solution :

Because each input value is paired with only one output value, the relationship given in the above mapping diagram is a function.

Note : 

In the above mapping diagram, b and c have the same output value. However, b has only one output value y and c also has only one output value y. Moreover, no input value has more than one output value. 

Example 4 :

Determine whether the relationship given in the mapping diagram is a function.

Solution :

Because each input value is paired with only one output value, the relationship given in the above mapping diagram is a function.

Example 5 :

Determine whether the relationship given in the mapping diagram is a function.

Solution :

Because the input value 3 is paired with more than one output value, the relationship given in the above mapping diagram is not a function.

Example 6 :

Determine whether the relationship given in the mapping diagram is a function.

Solution :

Because the input value c is not paired with any output value, the relationship given in the above mapping diagram is not a function.

Example 7 :

Is it possible for a function to have more than one input value but only one output value? Provide an illustration to support your answer.

Solution :

Yes, a function can possibly have more than one input value, but only one output value. 

Illustration :

In the above mapping diagram, there are three input values (1, 2 and 3). But there is only one out put value 4. 

According to the rule, each input value must have only one output value and no input value should have more than one output value. 

In the above mapping diagram, input value 1 has only one output value 4. The same has happened to the other two input values 2 and 3 also. No input value has more than one out put value. 

So, the relationship given in the above mapping diagram is a function. 

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