Ways of Describing Functions

We can describe a function in one of several ways. We've already seen a few such ways:

1. By describing the action of the function verbally. For example: "a function $f$ takes positive integers and squares them."
2. By using a math expression, also called formula, e.g., $f(x) = x^2$.
   This method is unambiguous, very precise, and powerful: to find the output for a certain input $x$, we simply plug $x$ into the formula of $f$ and get the output immediately.
3. By listing the pairs $(x, y)$ of the function, e.g., $f = \{(0, 0), (1, 1), (2, 4), (3, 9), \dots\}$.

Other ways of describing functions are:

4. By listing the coordinates of the points of the function in a table, e.g.:

   $x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$\dots$
   $f(x)$	$0$	$1$	$4$	$9$	$16$	$25$	$36$	$49$	$\dots$