Functions

# Functions - Functions 1 What is a RELATION? An Association...

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1 Functions

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What is a RELATION? An Association A Relationship e.g. “X is less than Y” “X is a factor of Y” “X is the mother of Y”
RELATION vs. FUNCTION Well-behaved Relation

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4 A function is a rule that assigns to each input member in a set to a unique output member in another set we call these assignments a function which we can denote by f, we say that “f is a function of A into B” which we write as f: A B Functions
5 Functions Def n : Suppose A is a non-empty set. if is an input element then the element in B which is assigned to a is denoted by f(a). Then we have a function. Let’s denote this function by f. A is said to be the domain of f. The domain of f is denoted by D(f). (collection of all the possible input members) A a

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6 not a function function A f e.g., D(f) = {1, 4, 7, 9}, f(1)=10, f(4)=0, f(7)=3, f(9)=6 not a function f f A A
7 Set which consists of all the members in B is call co-domain and set which consists of all outputs members is called the range(E) A B Domain Range Co-domain

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8 Function as a mapping from one set to another set If A and B are two sets then a function f of A into B is called a mapping of A into B. We say that f maps A into B and we write this as f: A B
9 if the domain and co-domain of a function f are the same set, then f: A A Then f is called a “transformation” on A

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10 Variables A variable that represent input numbers for a function is called an “independent variables” . A variable that represent output numbers for a function is called a “dependent variables” .
11 we say that the dependent variable is a function of the independent variable. Consider the bellow equation Y=2x+5 In this, x is the independent variable and y is the is the dependent variable. y is a function of x.

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12 Let A={1,2,3,4} B={1,2,3,4,5,6,7} Consider f: A B Where f(x)=x+2 The domain of the function is A and the co- domain is B. Range of f is f(1)=1+2=3 f(2)=2+2=4 f(3)=3+2=5 f(4)=4+2=6 that is Range E={3,4,5,6}
13 1 2 3 4 3 4 5 6 1 2 7 Domain Co-domain Range A B f

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14 Consider y 2 =x In this case y is not a function in x because when the input value of x is 9, y 2 =9 gives two output values y= +3 or -3. this goes same for x=4,16,25,…. .
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## This note was uploaded on 07/27/2011 for the course IT 1001 taught by Professor Sewwandi during the Spring '11 term at UCSC.

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Functions - Functions 1 What is a RELATION? An Association...

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