A function f, assigns exactly one value to every element x. We can think of x as the function"s input and y as its output. For our purposes, we can use y and f(x) interchangeably. In calculus 1, we deal with functions taking elements of the real numbers as inputs and outputting real numbers. We are primarily concerned with using graphs as visual representations of functions. Here are some definitions that are useful to keep in mind: Domain: the set of elements x that can be inputs for a function f. Range: the set of elements y that are outputs of a function f. Increasing function: a function is increasing over an interval a if for all , the property ( ) ( ) holds. Decreasing function: a function is decreasing over an interval a if for all , the property ( ) ( ) holds.