Mathematical Formulas for Industrial and Mechanical Engineering

5.17 Functions and Graphs

Relation R(x): A relation is a correspondence between two sets A and B such that

each element of set A corresponds to one or more elements of set B. Set A is called

the domain of the relation and set B is called the range of the relation.

Function f(x): A function is a relation such that for each element in the domain,

there corresponds exactly one and only one element in the range. In other words,

a function is a well-defined relation.

The function f ðxÞ5 a

n

x

n

1 a

n21

x

n21

1 a

n22

x

n22

1 ? 1 a

1

x 1 a

0

is a polynomial

function of degree n, where n is a nonnegative integer and a

0

; a

1

; a

2

; ...; a

n

are real

numbers. The domain of every