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