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.
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.