DETERMINE IF A RELATION IS A FUNCTION

About the topic "Determine if a relation is a function"

Determine if a relation is a function :

Here we are going to see, how to check whether the given relation is a function or not.

Let a ∈ A and b ∈ B, then the relation "R" from A to B can be defined as follows.

R  =  { (a, b) }

If this relation is a function, it has to satisfy the following two conditions.

(i) Each element of A has to be involved in mapping.

(ii) Each element of A has to be mapped to at most one element in B.

In other words,

(i) Each element of A must have an image in B.

(ii) Each element of A must have an unique image (not more than one image) in B.

If either of the above conditions is not met, then the relation is not a function.

There fore,

All the functions are relations. But all the relations need not be functions.

If a relation wants to be as a function, it has to meet the above two conditions.

Determine if a relation is a function - Examples

Example 1 :

In the above mapping from A to B, each element of A has an image in B. And also, each element of A unique image (not more than one image) in B.

Since, the above given relation meets both the conditions, it is a function.

Example 2 :

In the above mapping from P to Q, the element "c" in P does not have image in Q.

Since, the above given relation does not meet the first condition, it is not a function.

Example 3 :

In the above mapping from C to D, each element of C has an image in D.

But, the element 2 in C has two images (20, 40) in D, it does not meet the second condition. So, it is not a function.

Determine if a relation is a function - Vertical line test

Here, we are going to check, whether the given relation is a function using vertical line test.

Key concept :

A graph represents a function only if every vertical line intersects the graph in at most one point.

Example 1 :

Use the vertical line test to determine whether the following graph represents a function.

Solution :

Since the vertical line intersects the graph in at most one point, the given  graph represents a function.

Example 2 :

Use the vertical line test to determine whether the following graph represents a function.

Solution :

Since the vertical line intersects the graph in more than one point (three points), the given  graph does not represent a function.

After having gone through the stuff given above, we hope that the students would have understood , how to check whether a relation is a function.

Apart from the stuff given above, if you want to know more about "Determine if a relation is a function", please click here

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