Barrons AP Calculus

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1 Functions

CONCEPTS    AND SKILLS

In  this    chapter you will    review  precalculus topics. Although    these   topics  are

not directly    tested  on  the AP  exam,   reviewing   them    will    reinforce   some

basic   principles:

general properties  of  functions:  domain, range,  composition,    inverse;

special  functions:  absolute    value,  greatest    integer;    polynomial,

rational,   trigonometric,  exponential,    and logarithmic;

and the BC  topics,

parametrically  defined curves

polar   curves

Function    Domain  Range

A. DEFINITIONS

A1. A function f is a correspondence that associates with each element a of a
set called the domain one and only one element b of a set called the range. We
write

f   (a) =   b

to indicate that b is the value of f at a. The elements in the domain are called
inputs, and those in the range are called outputs.
A function is often represented by an equation, a graph, or a table.
A vertical line cuts the graph of a function in at most one point.

Example 1 __

The domain of f (x) = x^2 − 2 is the set of all real numbers; its range is the set of