**How do you figure out if a relation is a function ?**

If a relation has to be a function, it has to satisfy the following conditions.

(i) Domain of f is A.

(ii) For each x ∈ A, there is only one y ∈ B such that

(x, y) ∈ f .

Let us look into the following examples to understand the above concept.

**Example 1 :**

Does the following arrow diagrams represent a function? Explain.

**Solution :**

Every element in A has a unique image. Hence it is a function.

**Example 2 :**

Does the following arrow diagrams represent a function? Explain.

**Solution :**

C has two images namely 20 and 40. Hence, it is not a function.

**Example 3 :**

Let X = { 1, 2, 3, 4 }. Examine whether each of the relations given below is a function from X to X or not. Explain

f = { (2, 3), (1, 4), (2, 1), (3, 2), (4, 4) }

**Solution :**

To check whether the relation forms a function, it has to satisfy the above two conditions.

(i) Domain of f = {1, 2, 3, 4} = Set X

(ii) Every element in X must be associated with different elements. Here 2 is associated with two different elements 3 and 1.

Hence it is not a function.

**Example 4 :**

Which of the following relations are functions from A = { 1, 4, 9, 16 } to B = { –1, 2, –3, –4, 5, 6 }? In case of a function, write down its range.

f = { (1, –1), (4, 2), (9, –3), (16, –4) }

**Solution :**

To check whether the relation forms a function, it has to satisfy the above two conditions.

(i) Domain of f = {1, 4, 9, 16} = Set A

(ii) Each element in A is associated with elements in B.

Hence it is not a function.

Range = {-1, 2, -3, -4}

**Example 5 :**

If X = { 1, 2, 3, 4, 5 }, Y = { 1, 3, 5, 7, 9 } determine which of the following relations from X to Y are functions? Give reason for your answer. In case of a function, write down its domain, range and codomain.

R = { (1, 1), (2, 1), (3, 3), (4, 3), (5, 5) }

**Solution :**

To check whether the relation is a function, it has to satisfy the above two conditions.

(i) Domain of R = {1, 2, 3, 4, 5} = Set X

(ii) Every element in X has image in Y.

Hence it is not a function.

Domain = {1, 2, 3, 4, 5}

Range = {1, 3, 5}

Co domain = { 1, 3, 5, 7, 9 }

**Example 6 :**

Let A = { 10, 11, 12, 13, 14 }; B = { 0, 1, 2, 3, 5 } determine the following relations from X to Y are functions? Give reason for your answer.

f = { (10, 1), (11, 2), (12, 3), (13, 5), (14, 3) }

**Solution :**

To check whether the relation forms a function, it has to satisfy the above two conditions.

(i) Domain of f = {10, 11, 12, 13, 14} = Set A

(ii) Every element in A has image in B.

Hence it is not a function.

Let us see the next example on "How do you figure out if a relation is a function?".

**Example 7 :**

Does the following arrow diagrams represent a function? Explain.

**Solution :**

Every element in P has a unique image. Hence it is a function.

**Example 8 :**

Does the following arrow diagrams represent a function? Explain.

**Solution :**

Every element in P has a unique image. Hence it is a function.

After having gone through the stuff given above, we hope that the students would have understood " How do you figure out if a relation is a function?".

Apart from the stuff given above, if you want to know more about "How do you figure out if a relation is a function?", please click here.

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

HTML Comment Box is loading comments...

You can also visit our 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**