A function is a relation in which each input has only one output. In the relation , y is a function of x , because for each input x (1, 2, 3, or 0), there is only one output y . x is not a function of y , because the inputy = 3 has multiple outputs: x = 1 andx = 2 .

Examples:
\: y is a function of x , x is a function of y .

: y is not a function of x ( x = 3 has multiple outputs), x is a function of y .

: y is a function of x , x is not a function of y ( y = 9 has multiple outputs).

: y is not a function of x ( x = 1 has multiple outputs), x is not a function of y ( y = 2 has multiple outputs).

To determine whether y is a function of x , given a graph of a relation, use the following criterion: if every vertical lineyou can draw goes through only 1 point, y is a function of x . If you can draw a vertical line that goes through 2 points, yis not a function ofx . This is called the vertical line test.

Example 1: In the following graph, y is a function of x :

Functions and Relations
A function is one kind of interrelationship among objects. For every finite sequence of objects (called the arguments), a function associates a unique object (called the value). More formally, a function is defined as a set of finite lists of objects, one for each combination of possible arguments. In each list, the initial elements are the arguments, and the final element is the value. For example, the function contains the list , indicating that integer successor of is . A relation is another kind of interrelationship among objects in the universe of discourse. More formally, a relation is an arbitrary set of finite lists of objects (of possibly varying lengths). Each list is a selection of objects that jointly satisfy the relation. For example, the < relation on numbers contains the list , indicating that is less than . Note that both functions and relations are defined as sets of lists. In fact, every function is a relation. However, not every relation is...

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The Uses of DNA Technology in Forensic Science
Timothy Banas has a master's degree in biophysics and was a high school science teacher in Chicago for seven years. He has since been working as a trading systems analyst, standardized test item developer, and freelance writer. As a freelancer, he has written articles on everything from personal finances to computer technology.
Forensic science involves the use of scientific procedures to...

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BIAG NI LAM ANG (Epic of Ilocos Region)
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...late 90’s a new era has begun and NI has begun to flourish. One of the main reasons behind NI’s new found success and attractiveness is the events industry. There are always events taking place all over NI, and with each passing year, the number of events continues to grow, as does the prestige of many of the events that are held here.
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Epic Characteristics
● The epic used simple words that makes it easy to understand.
● The epic is unrealistic in the ff. parts of the epic:
1. Lam-ang was able to talk from the moment he was born.
2. So much dirt and so much evil was the smell taken of Lam-ang’s body, the fish in the river all died.
3. The white rooster’s crow made a house in the neighborhood immediately collapsed.
4. The dog’s growl made the collapsed house went up again as if...

...Jose Rizal’s Educational Background
Rizal’s first teachers:
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- was his mother she was patient, conscientious and , understanding
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- she encouraged him to write poems
2. Private Tutors of Rizal
- Maestro Celestino
- Maestro Lucas
- Leon Monroy
Rizal goes to Binan,Laguna:
- June, 1869 Rizal left for Binan
- Was accompanied by Paciano his older brother
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- In academic...

...PHILGOV
Reaction Paper : 2011 State of the Nation Address of President Benigno Aquino III
Last 25th of July this year, the State Of the Nation Address was held. As far as I remember, President Benigno Aquino III won last election maybe because of the help of the economic background of his parents contributed upon us. His advertisements were obviously all connected to his parents’ personal background.
Way back 1970’s, that is, the deceased Benigno Aquino (Ninoy) had fight...

...his father. Lam-ang defied the caveat and bravely fought with the chieftain and his tribesmen. The hero emerged victorious from the battle with little effort, finally avenging his murdered father.
(b) Author (origin of the story)
The Iloko Biag ni Lam-ang is the oldest recorded Philippine folk epic and the only complete epic to come down to us from the Christian Filipino groups. The earliest recording of the poem was given by Fr. Gerardo Blanco to Isabelo de los Reyes, who...

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