Dictionary for Basic and Intermediate Algebra
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Function

A relation is a rule of correspondence between two serts, that assigns to each element of the first set at least one element in the second set. The first set is called the Domain and the second set is called the Range. Thus you can consider that any set of ordered pairs is a relation.

Ex 1: The correspondence R, defined by 1R5, 2R3, 2R7, 4R 8, 5R8 is a relation..

This relation R, has Domain = {1,2,4,5} Range = { 5,3,7,8}and it can be written as
R = {(1,5), (2,3), (2,7), (4,8), (5,8)}

A function is a relation that assigns each element in the domain exactly one elemrnt in the range.

Remark: Letters f, g, h… are usually used to represent functions and f(x) is used to represent the value the function that assigns to x.
The relation R in the above example is not a function since 2 has assigned 3 and 7.

Remark: Letters f,g, h… are usually used to represent functions and f(x) is used to represent the value that the function assigns to x.

Ex 2: The function defined by , for x a real number, is usually written as
f(x) =2x+1. Find f(-2), f(0) & f(3).
Sol:

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