Domain and range

Definition

Domain is the set of all possible input values for a function, while range is the set of all possible output values. Together, they describe the scope of a function's operation.

5 Must Know Facts For Your Next Test

1. 1. The domain includes all x-values that make the function work without producing undefined results.
2. 2. The range includes all y-values that the function can produce.
3. 3. For rational functions, the domain excludes values that make the denominator zero.
4. 4. For square root functions, the domain includes only values where the expression inside the root is non-negative.
5. 5. A function's graph provides a visual way to determine both its domain and range.

Review Questions

• What is the domain of $f(x) = \frac{1}{x-2}$?
• How do you find the range of $g(x) = \sqrt{x+3}$?
• What is excluded from the domain of a logarithmic function?

Related terms

Function: A relation between sets that assigns to each element of a domain exactly one element of the range.

Interval Notation: A mathematical notation used to represent an interval as a pair of numbers, indicating its endpoints.

Asymptote: A line that a graph approaches but never touches or crosses.