A function f maps elements from a domain set X to a range set Y such that each element of X is mapped to exactly one element of Y. The domain is the set of all possible inputs, while the range is the set of possible outputs. An arrow diagram of a function must have an arrow from each element of X and no element of X can map to more than one element of Y. An example arrow diagram is given that satisfies these function properties by mapping elements of X={a,b,c} to unique elements of Y={1,2,3,4}. A non-function is also shown where an element of X is not mapped to any element of Y.

1. FUNCTION
Presented By:
 Muhammad Ahmad
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2. Function-Defination:
A function f from a set X to a set Y is a relationship
between elements of X and elements of Y such that
each element of X is related to a unique element of Y,
denoted f : X →Y. The set X is called the domain of f
and Y is called the
co-domain of f.
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3. Domain and Co-domain:
• The set of all all possible input values of a
Function is the Domain of f.
• The set of all all possible output values of a
Function is the Co-Domain of f.
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4. Arrow Diagram of a Function:
The definition of function implies that the arrow
diagram for a function ‘f’ has the following two
properties:
1. Every element of X has an arrow diagram
coming out of it.
2. No two elements of X has two arrows coming
out of it that point to two different element of
Y.
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5. Example:
Let X = {a,b,c} and Y= {1,2,3,4}
Define a function f from X to Y by the arrow diagram.
a.
b.
c.
.1
.2
.3
.4
f
X Y
You can easily note that the above diagram
satisfy the two conditions of a function
hence a graph of a function.
Note that f(a) = 2, f(b) = 4 and f(c) = 2
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6. Non Functions:
Which of the arrow diagrams define functions from X = {2,4,5}to Y =
{1,2,4,6}.
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2.
4.
5.
.1
.2
.4
.6
X Y
The relation given in the diagram (a) is
Not a function because there is no
out of 5∈X to any element of Y.

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