Big Idea:

Big Idea 4

Function families share similar graphs, behaviors, and properties.

1 week

Evidence of Understanding

  • identify similarities and differences among linear, quadratic, absolute value, and exponential function families based on features of their graphs or tables
    • interpret rate of change, domain and range patterns, minimums and maximums, intercepts, and symmetries for each type of function family
    • relate the rate of change and other key features of each function family to its parent function: f(x) = x (linear),  f(x) = x2  (quadratic), f(x) = |x| (absolute value) and f(x) = 2x (exponential)
       
  • compare functions within a family and describe transformations from the parent function
    • given a graphical representation of a parent function and another function in the same family, describe the vertical or horizontal shift and/or a dilation in the rate of change that happened (e.g., the graph shifted left 3 from the parent function)
    • compare tables of values for different functions within the same function family (the parent function and one other) (e.g., “I notice that the x-values in both tables stay the same but the corresponding  y-values are always 3 more than in the parent function’s table”)
    • create a graph or table of values for a function given the parent function and a stated transformation (NOTE: writing equations of transformations will wait until later units)
       
  • use linear, quadratic, exponential, piecewise or step functions to model situations
    • use the relationship between quantities in a situation to determine which function family provides the best model
      • analyze domain and range of different functions within the context of a situation to make sense of why certain functions have limitationson the domain and/or range

Develop conceptual understanding:

function family, parent function, linear function, quadratic function, absolute value function, exponential function, piecewise function, step function

Supporting terms to communicate:

function, f(x), axes, units, scale, coordinate point, ordered pair, table of values, rate of change, average rate of change, interval, increasing, decreasing, positive, negative, turning point, maximum, minimum, intercept, dependent, independent, domain, range, continuous, discrete, symmetry

Core Resource
A core resource supports multiple days of instruction. COMING SOON!
    Instructional Routine: Connecting Representations
    These tasks are embedded within the instructional routine called Connecting Representations.