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**FUNCTIONS AND RELATIONS **

**Definitions:**

A relation is a set of ordered pairs. An ordered pair has two compositions, the domain and the range. The domain are all

**x**in the set of ordered pairs and the range are all

**y**in the set of ordered pairs.

A function is a relation in which element of the domain (x) is paired with exactly one element of the range (y).

The domain of the function is the set consisting of all the first components in each element of a set

The range of the function is the set consisting of all the second components in each element of the set

Illustration for ordered pairs. All x's are colored in red as domain and all y's were colored in blue as range for clear description.

{ (1,3) ,(2,5), (3,6), (7,10) }

From this illustration the domain are (1,2,3,7) and the range are (3,5,6,10).

**Sample problem:**

1. State the domain and the range of the relation { (2,4) ,(5,6), (1,3), (6,10),(4,7) }.

Solution: Domain: ( 2,5,1,6,4)

Range : ( 4,6,3,10,7)

2. State the domain and the range of the relation { (a,1) ,(b,2), (c,3), (d,4),(e,5),(f,6) }.

Solution: Domain: ( a,b,c,d,e,f)

Range : ( 1,2,3,4,5,6)

3. State the domain and the range of the relation { (-2,1) ,(3,-2), (d,7), (-5,h),(e,5),(b,w) }.

Solution: Domain : ( -2,3,d,-5,e,b)

Range : ( 1,-2,7,h,5,w )

**EXERCISES:**

A. STATE WHETHER THE GIVEN IS A

2. [ (1,2), (3,-4), (5,6), (7,-8) ]

3. [ (2,3), (3,-4), (5,6), (,-8) ]

4. [ (1,2), (1,3), (1,4), (1,5) ]

B. Tell whether each of the following is a function or not.

1. Assign to each person his weight at an instance.

2. Assign to each person his weight at 5 different instances, each a moth apart.

3. Assign to each person his

*FUNCTION*OR A*RELATION*:**1. [ (2,3), (2,4), (3,4), (4,3) ]**

2. [ (1,2), (3,-4), (5,6), (7,-8) ]

3. [ (2,3), (3,-4), (5,6), (,-8) ]

4. [ (1,2), (1,3), (1,4), (1,5) ]

B. Tell whether each of the following is a function or not.

1. Assign to each person his weight at an instance.

2. Assign to each person his weight at 5 different instances, each a moth apart.

3. Assign to each person his

*(complete the sentence and find your answer).*