Domain

Definition

The domain of a function is the set of all possible input values (typically represented as 'x') that the function can accept. It determines the range of values for which the function is defined and produces real numbers.

5 Must Know Facts For Your Next Test

1. The domain is typically written in interval notation or set-builder notation.
2. To find the domain, look for values that make the function undefined, such as division by zero or taking even roots of negative numbers.
3. In polynomial functions, the domain is all real numbers because polynomials are defined for every real number.
4. For rational functions, exclude values that make the denominator zero from the domain.
5. In radical functions with an even index, exclude values that result in taking an even root of a negative number.

Review Questions

• What is the domain of the function f(x) = 1/(x-2)?
• How would you determine if -3 is in the domain of g(x) = √(x+2)?
• Identify any restrictions on the domain for h(x) = x^2 + 3x + 1.

Related terms

Range:

The set of all possible output values (typically represented as 'y') a function can produce.

Function:

A relation between a set of inputs and a set of permissible outputs where each input is related to exactly one output.

Interval Notation:

A way to represent subsets of real numbers using intervals to describe their start and end points.