Constant function

Definition

A constant function is a function that always returns the same value regardless of the input. It can be represented as $f(x) = c$, where $c$ is a constant.

5 Must Know Facts For Your Next Test

1. The graph of a constant function is a horizontal line.
2. The domain of a constant function is all real numbers, $\mathbb{R}$.
3. The range of a constant function is the single value $c$.
4. A constant function has no slope; its derivative is zero.
5. In interval notation, the range of a constant function $f(x) = c$ is written as $\{c\}$.

Review Questions

• What does the graph of a constant function look like?
• What are the domain and range of a constant function?
• How do you express a constant function in mathematical notation?

Related terms

Linear Function: A linear function represents a straight line and can be expressed in the form $f(x) = mx + b$, where $m$ and $b$ are constants.

Domain: The set of all possible input values (x-values) for which a given function is defined.

Range: The set of all possible output values (y-values) that result from using the inputs from the domain in a given function.