**Identifying and representing functions :**

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 or a table or a graph can be used to represent a relationship between input values and output values.

A mapping diagram or a table or a graph 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 :**

Since 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 :**

Since 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 :**

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

**Example 4 :**

Determine whether the relationship given in the table is a function.

**Solution :**

Since each input value is paired with only one output value, the relationship given in the above table is a function.

**Example 5 :**

Determine whether the relationship given in the table is a function.

**Solution :**

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

**Example 6 :**

Determine whether the relationship given in the table is a function.

**Solution :**

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

**Example 7 :**

The graph given below shows the relationship between the number of hours students spent studying for an exam and the marks scored in the exam. Determine whether the relationship represented by the graph is a function.

**Solution :**

From the graph, it is clear that if a students spends 2 hours for studying, he will be able to score 70 marks in the exam. And if he spends 9 hours for studying, he will be able to score 90 marks in the exam.

So, we can consider the number of hours of studying as input values and marks scored in the exam as output values.

The points represent the following ordered pairs in the form (input, output) or (x, y) :

(1, 70), (2, 70), (2, 85), (3, 75), (5, 80), (6, 82), (7, 88),aaaa(9, 90), (9, 95) and (12, 98).

In the above order pairs, there is only one output value for each input value. And no input value has more than one output value.

Since, there is only one output value for each input value, the relationship represented by the graph is a function.

**Example 8 :**

The graph shows the relationship between the heights and weights of the members of a basketball team. Is the relationship represented by the graph a function ? Explain.

**Solution :**

From the graph, it is clear that if the height of a member is 73 inches, his weight will be 180 lbs.

So, we can consider the height as input value and weight as output value.

The points represent the following ordered pairs in the form (input, output) or (x, y) :

(68, 160), (70, 165), (70, 175), (71, 170), (71, 185), (73, 180) and (74, 190).

Notice that 70 is paired with both 165 and 175, and 71 is paired with both 170 and 185. These input values are paired with more than one output value

Since, there is more than one output value for the input values 70 and 71, the relationship represented by the graph is not a function.

After having gone through the stuff given above, we hope that the students would have understood "Identifying and representing functions".

Apart from the stuff given above, if you want to know more about "Identifying and representing functions", please click here

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

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM 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**

**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**