Domain

Definition

The domain of a function is the complete set of possible input values (x-values) that allow the function to work within its constraints. It specifies the range of x-values for which the function is defined.

5 Must Know Facts For Your Next Test

1. The domain excludes any x-values that result in division by zero.
2. For square root functions, the domain includes only x-values that make the radicand non-negative.
3. Polynomials have domains that include all real numbers.
4. Rational functions can have domains restricted by their denominators.
5. The domain can often be found by identifying values that cause undefined expressions in the function.

Review Questions

• What is the domain of $f(x) = \frac{1}{x-3}$?
• How do you determine the domain of a square root function?
• What type of functions generally have a domain of all real numbers?

Related terms

Range:

The set of all possible output values (y-values) produced by a function based on its domain.

Function Notation:

A way to represent functions in the form $f(x)$, where $f$ denotes the function and $x$ represents an element from its domain.

Undefined: A term used to describe an expression or value that does not exist or cannot be computed within a given context, such as division by zero.