Big Idea:

Big Idea 3

Functions can be represented in multiple, equivalent ways.

1 week

Evidence of Understanding

  • analyze equivalent representations of the same function
    • identify characteristics of a function across different representations, especially end behavior, symmetry, critical points (including distinguishing mins and maxs as relative or absolute), zeros, rate of change, and increasing/decreasing/positive/negative intervals
      • Example: recognize increasing output values in the table correspond to an increasing interval on the graph, etc.
      • relate features of a parabola to features of its quadratic equation
      • relate the zeros of factorable polynomial functions to its equation (Note: this supports the Remainder Theorem in the Unit 4)
    • articulate and compare the advantages of different representations, including graphs, tables of values, equations, written descriptions, symbolic notations, etc.
  • create equivalent representations for a polynomial, exponential, piecewise or step function
    • identify missing characteristics for one representation using features from a different representation of the same function
    • create an equivalent representation given a graph, table of values, or situation
      • justify why both representations are equivalent
      • correctly label all important parts of each representation and describe how these labels translate across equivalent representations
      • use rates of change to generate equivalent representations
  • compare properties of two functions each represented in a different way
    • use general characteristics of function families to distinguish and compare the functions
    • describe characteristics that are similar and different
      • Example: identify which function has a larger maximum, more zeros, etc.  

Develop conceptual understanding:

end behavior, symmetry, critical point, zero, rate of change, polynomial function

Supporting terms to communicate:

domain, range, interval, intercepts, roots, relative/absolute min and max, linear, quadratic, exponential, logarithmic, square root, cube root, polynomial, rational, periodic

Core Resource

There is no Core Resource for this Big Idea.

Consider using the Instructional Routines linked below for teaching towards this Big Idea.

  • Exploring Equivalency
    This single-day resource supports students in finding equivalency across multiple representations of the same function.
    Exploring Equivalency

    For each card students are given two representations and explain how they are the same function. Then they complete the other representations that are missing so that each card will end up with:
    1. situation
    2. formula
    3. graph
    4. table
    5. function family 

    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.