Families of Functions

11 Components
Initial Task
Sorting Functions
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Functions & Situations
Re-engagement
End of Unit Assessments
End of Unit Assessment for Unit 1 Performance Task for Unit 1 End of Unit Assessment Teacher Resources ALG II Unit 1 Find aligned Regents questions with Quiz Banker
A2 U1: Families of Functions
Unit Outline
Initial Task
Sorting Functions
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Functions & Situations
Re-engagement
End of Unit Assessments
End of Unit Assessment for Unit 1 Performance Task for Unit 1 End of Unit Assessment Teacher Resources ALG II Unit 1 Find aligned Regents questions with Quiz Banker
None
A2 U1:

Families of Functions

How do different function families behave?
6 weeks
See Standards
Common Core: Major Standards:
F-IF.B.4

Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F-IF.B.6

Interpret functions that arise in applications in terms of the context. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F-BF.A.1a

Build a function that models a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context.

F-BF.A.1b

Build a function that models a relationship between two quantities.  Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

Common Core: Supporting Standards:
F-IF.C.7c

Analyze functions using different representations. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

F-IF.C.9

Analyze functions using different representations. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

F-LE.A.2

Linear, Quadratic, & Exponential Models: Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Common Core: Additional Standards:
F-BF.B.3

Build new functions from existing functions Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

F-LE.B.5

Interpret expressions for functions in terms of the situation they model. Interpret the parameters in a linear or exponential function in terms of a context.

Unit one is primarily about the descriptive, not the quantitative. The purpose of this unit is to build on students’ prior understanding of a function from Algebra 1 and develop a deeper understanding of how two quantities are related, how rates of change are compared, how functions are notated and described, and the ways we compare functions. The unit studies features of different functions and how to represent these in a variety of different ways—verbal description, functions rule, table, and graph. Real-life examples can be used to build and interpret functions and reinforce the multiple representations of functions.

Essential Questions:

  • What commonalities do functions within the same family have?
  • What makes a particular function family unique from other types of functions?
  • What do the key features of the graph of a function reveal about real world problems?
  • What families of functions have inverse functions for all real numbers?
Printable Unit Plan

Unit Outline

11 Components

Every unit begins with an Initial Task and ends with a Balanced Assessment, both focusing on core mathematics of the unit. The core mathematics is developed through a series of resources around Big Ideas; as you move through the unit, keep students focused on how these ideas are connected and how they address mathematical problem solving. Before attempting the Balanced Assessment, students have an opportunity to synthesize their knowledge through a multi-day Formative Assessment Lesson and teacher-designed re-engagement lessons.

Initial Task See 1 itemHide 1 item

Big Ideas See 5 itemsHide 5 items

Formative Assessment Lesson See 1 itemHide 1 item

Re-engagement See 0 itemsHide 0 items

End of Unit Assessments See 4 itemsHide 4 items