Big Idea:

Big Idea 1

The features of a periodic function repeat over a constant interval.

1 week

Evidence of Understanding

  • describe features of periodic functions
    • use features of the graph to describe patterns of a periodicfunction
      • use congruence to justify whether any given function is periodic or not
    • explain the domain and range of a periodic function from its graph or table
    • state the mins, maxs, and intercepts of a periodic function from its table or graph
      • create expressions to represent all of the mins, maxs, or x intercepts of a periodic function
    • describe the end behavior of a periodic function
    • recognize congruent chunks of a trig function and use the period to state repeating intervals that are increasing, decreasing, positive, or negative
       
  • describe features of a sine or cosine function from a table, graph, or function rule
    • identify congruent chunks of a trig function using the period, drawing lines of symmetry, and describing the transformations that carry parts of the function onto itself
    • use the graph’s scale to state the period of a trig function
      • Ex: state the period as 2π, 75o, 3.5, etc. by reading the scale on the graph
    • explain the domain and range of a trig function
      • identify the amplitude of a trig function from a function rule and its graph or table
      • describe how the midline and amplitude impacts the range of the trig function
    • state the mins, maxs, and intercepts of a trig function from its table or graph
      • recognize that all intercepts, mins, and maxs are equidistant from one another
      • create expressions to represent all of the mins, maxs, or x intercepts of a trig function
    • given a trig function rule, use calculator tools to describe features from the graph or table
    • describe the end behavior of a trig function

Develop conceptual understanding:

periodic function, period, trig function, amplitude, midline

Supporting terms to communicate:

function, scale, domain, range, intercepts, min, max, end behavior, interval, symmetry, equidistant, congruent, reflection, rotation, translation, transformation
Core Resource
A core resource supports multiple days of instruction.
  • Analyzing Periodic Functions
    This multiple-day resource supports students in recognizing and naming features of periodic functions.
    Resource:
    Analyzing Periodic Functions

    Students constructed a shared definition of a periodic function and describe features of periodic functions that are important to determining if a function is periodic or not. Students are also introduced to a specific periodic function, the cosine function, through analyzing its equation and graph. 

    All Resources From:
Instructional Routine: Contemplate then Calculate
These tasks are embedded within the instructional routine called Contemplate then Calculate.
Instructional Routine: Connecting Representations
These tasks are embedded within the instructional routine called Connecting Representations.
  • Cosine Graphs and Tables
    Students will be given different cosine graphs and must match them to the appropriate tables while noting what key points or features help them make connections and note the cyclical nature of both the tables and the graphs.
    Resource:
    Cosine Graphs and Tables

    Students will be given different cosine graphs and must match them to the appropriate tables while noting what key points or features help them make connections and note the cyclical nature of both the tables and the graphs.

    All Resources From: