College Algebra & Trigonometry, 2018a

Chapter 4
Functions
A function is generally defined as a relation in which each x value corresponds to
one and only one y value. This assigning of only one y value to each x is known
as “univalence.” The univalence requirement makes some manipulations in calculus
easier to work with and can be important in certain applications, but many
important relations (such as the hyperbola, circle and ellipse) are not univalent
and thus not functions.
A function typically describes a relationship between two sets. In our consideration
of functions these two sets will typically be real or complex numbers.
Functions are usually defined in one of several ways. They can be defined by (1)
a graph, (2) an algebraic relationship, (3) a rule or (4) a table of values. More than
one of these methods can be used to describe the same function.
4.1 Function Notation
The notation for a function is generally the f(x) notation. In learning about
graphing in algebra we typically use the x and y notation, that is: y =6x − 1.
In function notation, the dependent variable y is replaced by the notation f(x) :
f(x) =6x − 1
Function values for particular values of the independent variable x can be found
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