Function notation

#### Tier: #Higher

Description

Function notation is a concise way of writing mathematical relationships. $f(x)$ is read as "f of x" — the output of function $f$ when the input is $x$.

Reading function notation:

• $f(x) = 2x + 3$ means "the function $f$ maps $x$ to $2x + 3$"
• $f(4) = 2(4) + 3 = 11$ — substitute $x = 4$

Domain and range:

• The domain is the set of allowed input values
• The range is the set of possible output values

Example: $g(x) = x^2 - 1$ $$g(3) = 9 - 1 = 8, \quad g(-2) = 4 - 1 = 3$$

Function notation is used with Composite functions and Inverse functions.

Equation of a line: $f(x) = mx + c$ is an alternative way to write $y = mx + c$.

Common error: treating $f(x)$ as "$f$ multiplied by $x$" — it means the output of the function for input $x$.

Links

Substitution Equation of a straight line Composite functions Inverse functions