Function notation

Definition

Function notation is a way to represent functions in the form $f(x)$, where $f$ names the function and $x$ represents the input variable. It provides a concise and clear way to denote the output of a function given an input.

5 Must Know Facts For Your Next Test

1. In function notation, $f(x)$ denotes the value of the function $f$ at $x$.
2. Function notation can be used for any type of function, including linear, quadratic, polynomial, and more.
3. To evaluate a function using function notation, replace the input variable with the given number or expression.
4. The domain of a function is often specified in function notation as part of its definition.
5. Function composition can also be expressed using function notation, such as $(f \circ g)(x) = f(g(x))$.

Review Questions

• How do you evaluate $f(3)$ if $f(x) = x^2 + 2x + 1$?
• What does it mean when we write $g(a) = b$?
• Describe how you would express the composition of two functions $f$ and $g$ using function notation.

Related terms

Domain:

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

Range:

The set of all possible output values (usually y-values) that a function can produce.

$\text{Composition of Functions}$: $\text{Combining two functions where the output of one becomes the input for another, denoted as } (f \circ g)(x).$