Function

Definition

A function is a relation between a set of inputs and a set of permissible outputs where each input is related to exactly one output. It can be represented mathematically as $f(x)$, where $x$ is the input variable.

5 Must Know Facts For Your Next Test

1. A function passes the vertical line test; any vertical line should intersect the graph of the function at most once.
2. The domain of a function is the set of all possible input values (x-values) that make the function work.
3. The range of a function is the set of all possible output values (y-values) produced by the function.
4. $f(x) = x^2$ and $f(x) = \sin(x)$ are examples of functions.
5. Functions can be classified into different types such as linear, quadratic, polynomial, trigonometric, exponential, and logarithmic.

Review Questions

Related terms

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) resulting from using the domain in a given function.

Vertical Line Test: A method to determine if a graph represents a function by checking if any vertical line intersects the graph more than once.