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Quick review of functions
SC105 (DAIICT) Review of functions 30 July, 2008 1 / 3
http://find/http://goback/
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Quick review of functions
A function f: X Yis a rule which assigns an element of the setY
to every element of the set X.
SC105 (DAIICT) Review of functions 30 July, 2008 1 / 3
http://find/http://goback/
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Quick review of functions
A function f: X Yis a rule which assigns an element of the setY
to every element of the set X.
SC105 (DAIICT) Review of functions 30 July, 2008 1 / 3
http://find/http://goback/
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Quick review of functions
A function f: X Yis a rule which assigns an element of the setY
to every element of the set X.
Xis the domain of the function f.
SC105 (DAIICT) Review of functions 30 July, 2008 1 / 3
http://find/http://goback/
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Quick review of functions
A function f: X Yis a rule which assigns an element of the setY
to every element of the set X.
Xis the domain of the function f.
Yis the co-domain of the function f.
SC105 (DAIICT) Review of functions 30 July, 2008 1 / 3
http://find/http://goback/
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Quick review of functions
A function f: X Yis a rule which assigns an element of the setY
to every element of the set X.
Xis the domain of the function f.
Yis the co-domain of the function f.
Functions are also called mappings/transformations/operator
.
SC105 (DAIICT) Review of functions 30 July, 2008 1 / 3
http://find/http://goback/
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Quick review of functions
A function f: X Yis a rule which assigns an element of the setY
to every element of the set X.
Xis the domain of the function f.
Yis the co-domain of the function f.
Functions are also called mappings/transformations/operator
.
x AAAAA f(x).
SC105 (DAIICT) Review of functions 30 July, 2008 1 / 3
http://find/http://goback/
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8/28
Quick review of functions
A function f: X Yis a rule which assigns an element of the setY
to every element of the set X.
Xis the domain of the function f.
Yis the co-domain of the function f.
Functions are also called mappings/transformations/operator
.
x AAAAA f(x). The set of output values (a subset of Y) iscalled
the range of the function f.
SC105 (DAIICT) Review of functions 30 July, 2008 1 / 3
http://find/http://goback/
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Quick review of functions
A function f: X Yis a rule which assigns an element of the setY
to every element of the set X.
Xis the domain of the function f.
Yis the co-domain of the function f.
Functions are also called mappings/transformations/operator
.
x AAAAA f(x). The set of output values (a subset of Y) iscalled
the range of the function f. Notn.: f(X).
SC105 (DAIICT) Review of functions 30 July, 2008 1 / 3
http://find/http://goback/
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10/28
Quick review of functions
A function f: X Yis a rule which assigns an element of the setY
to every element of the set X.
Xis the domain of the function f.
Yis the co-domain of the function f.
Functions are also called mappings/transformations/operator
.
x AAAAA f(x). The set of output values (a subset of Y) iscalled
the range of the function f. Notn.: f(X).
Some functions with special properties are
onto/surjective,one-one/injective, one-one
correspondence/bijective
SC105 (DAIICT) Review of functions 30 July, 2008 1 / 3
http://find/http://goback/
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Quick review of functions
A function f: X Yis a rule which assigns an element of the setY
to every element of the set X.
Xis the domain of the function f.
Yis the co-domain of the function f.
Functions are also called mappings/transformations/operator
.
x AAAAA f(x). The set of output values (a subset of Y) iscalled
the range of the function f. Notn.: f(X).
Some functions with special properties are
onto/surjective,one-one/injective, one-one
correspondence/bijective
A SurjectionSC105 (DAIICT) Review of functions 30 July, 2008 1 /
3
http://find/http://goback/
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Quick review of functions
A function f: X Yis a rule which assigns an element of the setY
to every element of the set X.
Xis the domain of the function f.
Yis the co-domain of the function f.
Functions are also called mappings/transformations/operator
.
x AAAAA f(x). The set of output values (a subset of Y) iscalled
the range of the function f. Notn.: f(X).
Some functions with special properties are
onto/surjective,one-one/injective, one-one
correspondence/bijective
A Surjection An injection
SC105 (DAIICT) Review of functions 30 July, 2008 1 / 3
http://find/http://goback/
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Quick review of functions
A function f: X Yis a rule which assigns an element of the setY
to every element of the set X.
Xis the domain of the function f.
Yis the co-domain of the function f.
Functions are also called mappings/transformations/operator
.
x AAAAA f(x). The set of output values (a subset of Y) iscalled
the range of the function f. Notn.: f(X).
Some functions with special properties are
onto/surjective,one-one/injective, one-one
correspondence/bijective
A Surjection An injection A bijection
SC105 (DAIICT) Review of functions 30 July, 2008 1 / 3
http://find/http://goback/
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Real Functions
SC105 (DAIICT) Review of functions 30 July, 2008 2 / 3
http://find/http://goback/
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Real Functions
Domain and range are subsets ofR.
SC105 (DAIICT) Review of functions 30 July, 2008 2 / 3
http://find/http://goback/
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Real Functions
Domain and range are subsets ofR.
Common representation: y= f(x) - called formula/expression .
SC105 (DAIICT) Review of functions 30 July, 2008 2 / 3
http://find/http://goback/
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Real Functions
Domain and range are subsets ofR.
Common representation: y= f(x) - called formula/expression .
In the formula, xis called the independent variable ,
SC105 (DAIICT) Review of functions 30 July, 2008 2 / 3
R l F i
http://find/http://goback/
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Real Functions
Domain and range are subsets ofR.
Common representation: y= f(x) - called formula/expression .
In the formula, xis called the independent variable , yis called
the
dependent variable .
SC105 (DAIICT) Review of functions 30 July, 2008 2 / 3
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R l F ti
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Real Functions
Domain and range are subsets ofR.
Common representation: y= f(x) - called formula/expression .
In the formula, xis called the independent variable , yis called
the
dependent variable .When the domain is not explicitly defined,
the natural domain (largestset of real numbers for which the
formula is defined) is assumed.
The range can be determined by using the formula (range=set
of
possible values of the dependent variable).
SC105 (DAIICT) Review of functions 30 July, 2008 2 / 3
G hi l t ti f l f ti
http://find/http://goback/
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Graphical representation of real functions
SC105 (DAIICT) Review of functions 30 July, 2008 3 / 3
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Graphical representation of real functions
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Graphical representation of real functions
Vertical line test
If a vertical line intersects a graph in more than one point,
the graph is notthe graph of a function.
SC105 (DAIICT) Review of functions 30 July, 2008 3 / 3
Graphical representation of real functions
http://find/http://goback/
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Graphical representation of real functions
Vertical line test
If a vertical line intersects a graph in more than one point,
the graph is notthe graph of a function. i.e, Straight lines
(with-in the domain) parallel tothe y-axis must cut the graph at
only one point.
SC105 (DAIICT) Review of functions 30 July, 2008 3 / 3
Graphical representation of real functions
http://find/http://goback/
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Graphical representation of real functions
Vertical line test
If a vertical line intersects a graph in more than one point,
the graph is notthe graph of a function. i.e, Straight lines
(with-in the domain) parallel tothe y-axis must cut the graph at
only one point.
y= x3
SC105 (DAIICT) Review of functions 30 July, 2008 3 / 3
http://find/http://goback/
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Graphical representation of real functions
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Graphical representation of real functions
Vertical line test
If a vertical line intersects a graph in more than one point,
the graph is notthe graph of a function. i.e, Straight lines
(with-in the domain) parallel tothe y-axis must cut the graph at
only one point.
y= x3 " x2a2
+ y2
b2= 1 %
SC105 (DAIICT) Review of functions 30 July, 2008 3 / 3
http://find/http://goback/
