# IDENTIFYING FUNCTIONS FROM TABLES

## About "Identifying functions from tables"

Identifying functions from tables :

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

Relationships between input values and output values can also be represented using tables. The values in the first column are the input values. The values in the second column are the output values. The relationship represents a function if each input value is paired with only one output value.

## Identifying functions from tables - Examples

Example 1 :

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 2 :

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 3 :

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.

Note :

In the above table, 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 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.

According to the rule of the function, there must be an output value for each input value. Since there is no output value for the input value "c", the relationship given in the above table is not a function.

Example 7 :

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 8 :

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 table, there are five input values values (1, 2, 3, 4 and 5). But there is only one out put value 6.

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 table, input value 1 has only one output value 6. The same has happened to the other input values 2, 3, 4 and 5 also. No input value has more than one out put value.

Hence, the relationship given in the above table is a function.

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

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

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6