SECTION
T
he first functions to which you are typically exposed are those described by sets of ordered pairs that
can be visualized in the Cartesian plane. Such functions are generally described using either algebraic
expressions or graphs, and are denoted using letters, such asfor g. When we want to emphasize the input-
output defining relationship of a function, an expression of the form y= f(x) is often used. The arithmetic of real-
valued functions is performed using the arithmetic of real numbers and algebraic expressions.
The domainof a function can be thought of as the set of all possible x-values for which there corresponds
an output y. From the graphical viewpoint, an x-value belongs to the domain offif an ordered pair with that
x-value belongs to the graph off. When an algebraic expression is used to describe a function y= f(x), it is con-
venient to view the domain as the set of all values ofxthat can be substituted into the expression and yield a mean-
ingful output. The rangeof a function is the set of all possible y-values attained at some member of the domain.
Basic functions and their properties are reviewed in the ten problem sets that make up this section.6
ELEMENTARY
FUNCTIONS