In Module 3, Topic B, students connect their understanding of functions to their knowledge of graphing from Grade 8. They learn the formal definition of a function and how to recognize, evaluate, and interpret functions in abstract and contextual situations (F-IF.A.1, F-IF.A.2). Students examine the graphs of a variety of functions and learn to interpret those graphs using precise terminology to describe such key features as domain and range, intercepts, intervals where the function is increasing or decreasing, and intervals where the function is positive or negative. (F-IF.A.1, F-IF.B.4, F-IF.B.5, F-IF.C.7a).
In Module 3, Topic D, students apply and reinforce the concepts of the module as they examine and compare exponential, piecewise, and step functions in a real-world context (F-IF.C.9). They create equations and functions to model situations (A-CED.A.1, F-BF.A.1, F-LE.A.2), rewrite exponential expressions to reveal and relate elements of an expression to the context of the problem (A-SSE.B.3c, F-LE.B.5), and examine the key features of graphs of functions, relating those features to the context of the problem (F-IF.B.4, F-IF.B.6).
Module 5, Topic A focuses on the skills inherent in the modeling process: representing graphs, data sets, or verbal descriptions using explicit expressions (F-BF.A.1a) when presented in graphic form in Lesson 1, as data in Lesson 2, or as a verbal description of a contextual situation in Lesson 3. They recognize the function type associated with the problem (F-LE.A.1b, F-LE.A.1c) and match to or create 1- and 2-variable equations (A-CED.A.1, A-CED.2) to model a context presented graphically, as a data set, or as a description (F-LE.A.2). Function types include linear, quadratic, exponential, square root, cube root, absolute value, and other piecewise functions. Students interpret features of a graph in order to write an equation that can be used to model it and the function (F-IF.B.4, F-BF.A.1) and relate the domain to both representations (F-IF.B.5). This topic focuses on the skills needed to complete the modeling cycle and sometimes uses purely mathematical models, sometimes real-world contexts.