Unit 4: Functions

Definition of a Function: Students will understand that a function is a rule assigning exactly one output to each input.  

Representation Forms: They will recognize functions in various forms, including algebraic, graphic, tabular, and verbal descriptions.  

Function Characteristics: Students will be able to identify domain and range, input/output pairs, and independent vs. dependent variables.

Identification: They will learn to distinguish between linear functions (which form a straight line and follow y = mx + b) and nonlinear functions.

Comparative Analysis: Students will know how to compare properties of two different functions represented in different ways.

Define and Identify Functions:
Use the vertical line test on graphs and check for repeated inputs in tables to determine if a relation is a function.

Translate Between Representations:
Convert function data between ordered pairs, tables, mapping diagrams, and coordinate grids.

Analyze Linear vs. Nonlinear:
Compare the rates of change of different functions to identify which are linear (y=mx+b).

Model Real-World Scenarios: Construct a function to model a linear relationship between two quantities, such as distance over time.

Interpret Graphs Qualitatively:
Describe where a graph is increasing or decreasing and locate the intercepts.

• Function Classification Task: Correcting a set of "non-functions" and explaining why they fail the vertical line test (single output rule).

• Comparative Performance Task: Analyzing two different cell phone plans—one given as a table and one as an equation—to find the initial value and rate of change for both.

• Graph Storytelling: Students use a graph based on a verbal description of a trip (e.g., stopping for gas, driving on a highway) and label parts as increasing, decreasing, or constant.