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Functions are a fundamental concept in all mathematics courses, including calculus. You need to understand of how to describe the domain, describe the range, describe the rule, and form composite functions.

A FUNCTION is a rule, usually written algebraically like
y=3x-2, that assigns each number in a DOMAIN to exactly one number in the
RANGE.

For example, ,
the domain of this function is all real numbers, and the range is all
non-negative real numbers (zero and all positive real numbers).** **The
rule is to first square the number in the domain and then take the
principal square root (positive answer only) of the answer.

A composite function is denoted .

Meaning: A number x is placed in the function f first and then that result is placed in the function g. The final results is g(f(x)).

*Check Your
Understanding:* (Remember to write down your answers to these
questions.)

Describe the domain and range of f and g. Then form the function f(g(x)) and describe the domain and range of this composed function, if

1. and

2. and

3. and

This page was last modified on 03/21/16

© Rahn, 2000