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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) = x^{2} (quadratic), f(x) = |x| (absolute value) and f(x) = 2^{x} (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 limitations on the domain and/or range