Unit 1: Polynomial & Rational Functions

In Unit 1, students develop understanding of two key function concepts while exploring polynomial and rational functions. The first concept is covariation, or how output values change in tandem with changing input values. The second concept is rates of change, including average rate of change, rate of change at a point, and changing rates of change. The central idea of a function as a rule for relating two simultaneously changing sets of values provides students with a vital tool that has many applications, in nature, human society, and business and industry. For example, the idea of crop yield increasing but at a decreasing rate or the efficacy of a medicine decreasing but at an increasing rate are important understandings that inform critical decisions.  In other words, topics may include:

• Describing how quantities change with respect to each other

• Describing end behavior of polynomial and rational functions

• Identifying asymptotes of and holes in the graphs of rational functions

• Modeling aspects of scenarios using polynomial and rational functions

• Identifying assumptions and limitations of function models