Big Idea:

Big Idea 5

Functions within a family are transformations of the parent function.

1 week

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.
  • Transformations of Different Families of Functions
    This single-day resource supports students in transforming functions.
    Resource:
    Transformations of Different Families of Functions

    This single-day resource supports students in transforming functions. It includes cards with examples of transformations for functions from different function families for students to fill in missing information.

    All Resources From:
Instructional Routine: Contemplate then Calculate
These tasks are embedded within the instructional routine called Contemplate then Calculate. COMING SOON!
    Instructional Routine: Connecting Representations
    These tasks are embedded within the instructional routine called Connecting Representations.
    • Transformations of Graphs and Tables
      Connect what students know about transformations to transformations of functions in both graph, table, and function notation format.
      Resource:
      Transformations of Graphs and Tables

      Connect what students know about transformations to transformations of functions in both graph, table, and function notation format.

      All Resources From: