Function (Encyclopedia of Science)
A function is a mathematical relationship between two sets of real numbers. These sets of numbers are related to each other by a rule that assigns each value from one set to exactly one value in the other set. For example, suppose we choose the letter x to stand for the numbers in one set and the letter y for the numbers in the second set. Then, for each value we assign to x, we can find one and only one comparable value of y.
An example of a function is the mathematical equation y = 3x + 2. For any given value of x, there is one and only one value of y. If we choose 5 for the value of x, then y must be equal to 17 (3 · 5 + 2 = 17). Or if we choose 11 for the value of x, then y must be equal to 35 (3 · 11 + 2 = 35).
The standard notation for a function is y = f(x) and is read "y equals f of x." Functions can also be represented in other ways, such as by graphs and tables. Functions are classified by the types of rules that govern their relationships: algebraic, trigonometric, logarithmic, and exponential. Mathematicians and scientists have found that elementary functions represent many real-world phenomena.
Characteristics of functions
The idea of a function is very important in mathematics because it describes any situation in which one quantity depends on another. For example, the height of a person depends, to a...
(The entire section is 960 words.)
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