Big Idea:

Big Idea 4

Functions belonging to the same family share similar graphs, behaviors, and characteristics.

1 week

Evidence of Understanding

  • compare linear, quadratic, absolute value, and exponential function families
    • interpret rate of change, domain and range patterns, minimums and maximums, intercepts, and symmetries for each type of function family
    • identify similarities and differences based on features of their graphs or tables


  • 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 limitations on the domain and/or range
    • apply rate of change to choose and justify an appropriate function model
      • recognize situations best modeled by linear functions in which one quantity changes at a constant rate per unit interval
      • recognize situations best modeled by exponential functions as compared to linear or quadratic models  


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.