Objectives: The basic object of study in calculus is a function. We will start with the definition of a function and examine the representation in four modes: symbolic, numerical, graphical and verbal. The domain and range of a function are also defined; exercises on finding the domain of a function are provided.

Working through these materials, the student should be able

• to understand the four representations of a function;
• to recognize a function in each of these representations;
• to use function notation;
• to calculate the domain of a function; and
• to determine whether a given number is in the range of a function.

Modules:

 DEFINITION. A function is a rule or correspondence which associates to each number x in a set A a unique number f(x) in a set B. The set A is called the domain of f and the set of all f(x)'s is called the range of f.

• Discussion [Using Flash]

• Four representations of a function:
1. Symbolic or algebraic
Discussion [Using Flash]
2. Numerical
Discussion [Using Flash]
3. Graphical
Discussion [Using Flash]
4. Verbal
Discussion [Using Flash]

• Drill on finding the domains of functions.