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.

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.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**