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 in the coordinate plane.
2. Its slope is zero because there is no change in the $y$-value as $x$ changes.
3. The domain of a constant function is all real numbers, denoted as $(-\infty, \infty)$.
4. The range of a constant function is the single value $\{c\}$.
5. Constant functions are both even and odd functions because they are symmetric about both the y-axis and the origin.

Review Questions

• What does the graph of a constant function look like?
• What is the slope of a constant function and why?
• What are the domain and range of a constant function?

Related terms

Linear Function:

A linear function has the form $f(x) = mx + b$, where $m$ and $b$ are constants. Its graph is a straight line.

Horizontal Line: A horizontal line has an equation of the form $y = c$, where $c$ is a constant. This represents a constant function.

$y$-intercept: $y$-intercept is the point where the graph intersects with the y-axis. For a constant function, this occurs at $(0, c)$.