Function Notation

Property When a dependent variable $y$ is a function of an independent variable $x$, it can be written as $y = f(x)$. For example, $y = 6x + 3$ is the same as $f(x) = 6x + 3$.

Examples The equation $y = 2x 5$ can be written in function notation as $f(x) = 2x 5$. To find the value when $x=3$ for $f(x) = 4x$, we write $f(3) = 4(3) = 12$. If a movie ticket costs 15 dollars, the cost function can be written as $C(t) = 15t$, where $t$ is the number of tickets.

Explanation Function notation, like $f(x)$, is just a fancy way of saying that an equation is a function. The letter 'f' is the name of the function, and the variable in the parentheses, like $(x)$, is the input. It helps us see the relationship between the input and the output clearly, like a label on a machine.