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
Browse 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
Big Idea:

Big Idea 5

Functions within a family are transformations of the parent function.

1 week
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.

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.

Evidence of Understanding

  • compare functions within a family and describe the transformations from the parent function
    • describe transformations between the parent function and another function in the same family
      • describe the translation (vertical or horizontal shift), reflection over a line, or dilation in the rate of change
      • use words or symbolic notations
      • Example: The graph shifted up 3 from the parent function and in the table of values the outputs are 3 units higher compared to the parent function.
    • create a graph, table of values, or equation for a function given the parent function and a stated transformation
  • describe how transformations impact the zeros, critical points, and rate of change of a function
    • describe how points of a function change as a result of a given transformation
      • identify what stays the same and what is different
    • explain how translations, f(x) + k or f(x + k), and reflections, f(x) or f(-x), preserve distances within the original function but only translations preserve orientation
    • explain how dilations, k ● f(x), impact the instantaneous rate of change for all points of a function except the mins and maxs

Develop conceptual understanding:

transformation, parent function, translation, reflection, dilation

Supporting terms to communicate:

input, output, independent, dependent, domain, range, symmetry, rate of change, end behavior, interval, intercepts, zeros, roots, critical points, linear, absolute value, quadratic, cubic, polynomial, square and cube root, exponential, logarithmic, periodic, rational 

Core Resource
A core resource supports multiple days of instruction.
Instructional Routine: Connecting Representations
These tasks are embedded within the instructional routine called Connecting Representations.