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. It provides a clear and concise way to denote the relationship between variables.

5 Must Know Facts For Your Next Test

1. In function notation, $f(x)$ denotes that $f$ is a function of $x$, where $x$ is the input variable.
2. The expression $f(a)$ means you substitute $a$ for every occurrence of $x$ in the function definition.
3. Function notation allows for easy evaluation of functions at specific points and comparison of different functions.
4. It simplifies expressing operations on functions, such as addition, subtraction, multiplication, and composition of functions.
5. Common forms include polynomial functions like $f(x) = x^2 + 3x + 2$, trigonometric functions like $g(x) = \sin(x)$, and exponential functions like $h(x) = e^x$.

Review Questions

• What does the notation $f(3)$ represent if you have a function defined as $f(x) = x^2 + 1$?
• How can you use function notation to evaluate the function at multiple points?
• If given two functions in notation form, how can you express their sum using function notation?

Related terms

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

Range: The set of all possible output values $(y)$ produced by a function from its domain.

$Composite Function (g \circ f)(x)$: $A composite function is formed when one function is applied to the result of another. If f and g are two functions, then (g \circ f)(x) = g(f(x)).$