Unit 1: Polynomial and Rational Functions

Functions and How Quantities Change in Tandem

A function is a mathematical relationship that maps a set of input values to a set of output values such that each input value is mapped to exactly one output value. The input values are the domain (often the independent variable, x), and the output values are the **range** (often the dependent variable, y). The input and output of a function vary according to the function rule, and that relationship can be represented graphically, verbally, analytically, or numerically.

A graph is a visual display of input-output pairs. It helps you see how outputs change as inputs change, including where the function increases/decreases, where it crosses the axes, and how its overall shape behaves.

A function is increasing over an interval of its domain if, as input values increase, output values always increase. Formally, for all a and b in the interval, if a