Evidence of Understanding

**analyze the rate of change and initial value on a function’s table or graph and use them to describe characteristics about the function**- determine the
**intercepts**exactly (for integers) or approximately, from a table or graph - justify whether given values belong in the domain or range of the function
- estimate the
**rate of change**from a linear, exponential, piecewise, step, or absolute value graph- use the rate of change to describe patterns for different function families

- analyze how transformations impact the function’s graph and table (emphasis on dilations to the rate of change and/or translations of the initial value)

- determine the

**compare linear and exponential function families using rate of change**- distinguish situations and number sequences (esp.
**arithmetic**and**geometric**) that are best modeled by**linear**,**exponential**or other functions- recognize and apply vocabulary to describe linear or exponential rate of change
*(Example: decay, compound, fixed rate, etc.)*

- recognize and apply vocabulary to describe linear or exponential rate of change
- recognize when quantities changes at a constant rate relative to one another
- show that a quantity increasing exponentially eventually exceeds a quantity increasing linearly
- analyze examples and nonexamples to define linear functions as growing by equal differences over equal intervals, and exponential functions growing by equal factors over equal intervals

- distinguish situations and number sequences (esp.

**use a function’s rate of change to predict future states/generate next steps**- use the rate of change to determine specific output or input values (given the other) from a situation, graph, table, or number sequence
- calculate and describe the meaning of the average rate of change in relation to context
- recognize when the average rate of change is zero and describe its meaning

- describe the rate of change patterns using words for
**recursive**and**explicit**forms - accurately graph a linear or exponential function and label its intercepts given at least three coordinate pairs and justify reasoning

Develop conceptual understanding with these terms:

rate of change, slope, initial value, y intercept, x intercept, arithmetic sequence, geometric sequence, linear, exponential, recursive

Support students in using these terms:

function, average rate of change, interval, dependent, independent, input, output, domain, range, integer, continuous, discrete, function family