Evidence of Understanding

**interpret a situation, graph, table of values, or equation using the rate of change**- calculate and interpret
**average rate of change**in relation to a context- explain the meaning of an average rate of change equal to zero, and when appropriate, make connections between the zero change and the graph’s symmetry and critical points

- recognize a
**constant rate of change**in a table of values, graph, or situation - describe rate of change in relation to critical points or increasing/decreasing intervals
*Example: when the rate of change is positive the function is increasing, negative when decreasing and approaches zero as it gets closer to a min or max*- estimate the
**instantaneous rate of change**through a point on the function using the qualities of the**tangent line**

- interpret real world behavior using a function's average or instantaneous rate of change

- calculate and interpret
**determine which function families best model given sets of real world data**- compare linear, quadratic, and exponential functions using the rate of change
*Example:***exponential functions**grow by equal factors over equal intervals and the second difference ('rate of change of the rate of change') for quadratic functions is constant

- use the rate of change to determine which function family fits best
- relate key quantities in a situation to key characteristics of a function family and their graphs
*(especially linear, quadratic, or exponential functions)* - create a graph, table of values, or an equation that best models a situation and use the model to evaluate the situation (find a missing value, make a prediction, etc.)

- compare linear, quadratic, and exponential functions using the rate of change

Develop conceptual understanding:

average rate of change, constant rate of change, instantaneous rate of change, tangent line, exponential functionSupporting terms to communicate:

end behavior, symmetry, zero, root, intercept, critical point, relative or absolute min/max interval, linear, quadratic, logarithmic, square root, cube root, polynomial, rational, periodic, step function