Big Idea:

Big Idea 1

Function families share similar graphs, behaviors, and properties.

1 week

Evidence of Understanding

  • compare the general shape and behavior of different function types
    • identify intervals of a function that are increasing, decreasing, positive or negative
      • use words, equations/inequalities, and interval notation
      • generalize how intervals distinguish different function families (Example: quadratics always have one increasing interval and one decreasing interval)
    • predict end behavior using a graph’s shape and the function’s rate(s) of change
      • explain why the end behavior of a periodic function is undefined
    • use symmetry from a function’s graph or table to distinguish function families
       
  • identify and analyze points that determine the shape and behavior of a function’s graph
    • determine exact integer zeros and approximate non-integer zeros from a graph or table
      • recognize when a function is periodic and use the repetition to describe zeros of a periodic function
    • recognize zeros (x intercepts) separate positive and negative intervals
    • describe why critical points (mins and maxs) separate increasing and decreasing intervals
    • use end behavior to distinguish relative from absolute mins and maxs
    • create the graph for a given function rule using its intercepts, mins, maxs, and end behavior
      • use tools strategically, especially graphing calculator features  
      • algebraically solve for key points of a linear or quadratic equation (using Algebra 1)
         
  • determine a function’s family using its key points, shape, and end behavior
    • describe and predict general features of critical points and zeros for each function family
      • Example: cubics have at most 3 x-intercepts, quadratics always have 1 absolute min or max, etc.
    • describe characteristics of a function’s graph or sketch the possible graph of a function given  its characteristics
    • recognize a periodic function from its undefined end behavior, repeating points or shape

Develop conceptual understanding:

increasing interval, decreasing interval, positive interval, negative interval, end behavior, symmetry, zero, periodic function, critical point, relative or absolute min/max

Supporting terms to communicate:

linear, absolute value, quadratic, cubic, square root, cube root, polynomial, exponential, logarithmic, rational, piecewise, step function, integer

CORE RESOURCE
A core resource supports multiple days of instruction.
  • Function Features
    A multiple-day resource that supports students in grappling with the way a graph's shape and key points distinguish function families.
    Resource:
    Function Features

    A multiple-day resource that supports students in grappling with the way a graph's shape and key points distinguish function families.  

    All Resources From:
INSTRUCTIONAL ROUTINE: CONNECTING REPRESENTATIONS
These tasks are embedded within the instructional routine called Connecting Representations.