Home > Encyclopedia of Science > Function

• Characteristics of functions
• Words to Know
• Classification of functions
• Applications

A function is a mathematical relationship between two sets of real numbers. These sets of numbers are related to each other by a rule that assigns each value from one set to exactly one value in the other set. For example, suppose we choose the letter x to stand for the numbers in one set and the letter y for the numbers in the second set. Then, for each value we assign to x, we can find one and only one comparable value of y.

An example of a function is the mathematical equation y = 3x + 2. For any given value of x, there is one and only one value of y. If we choose 5 for the value of x, then y must be equal to 17 (3 · 5 + 2 = 17). Or if we choose 11 for the value of x,...