Evidence of Understanding

**construct an explicit or recursive function rule from a situation, graph, or table of values**- describe how quantities from the situation, table, or graph map to parts of the equation
- distinguish
**exponential growth**from**exponential decay**and describe the percentage at which the function is increasing or decreasing

- distinguish
- create and justify linear or exponential function rules using rate of change
- differentiate y = mx + b (product mx because of
__repeated addition__) from y =a∙b^{x}(**base**and**exponent**b^{x}because of__repeated multiplication__) - explain why the rate of change is multiplied (mx) and initial value is added (+b) for linear function rules in the form f(x) = mx + b

- differentiate y = mx + b (product mx because of
- analyze arithmetic and geometric sequences and write a rule to best model the sequence
- use the rate of change between each term to explain sequences as a discrete linear or discrete exponential function

- create an absolute value function rule and describe the connections to a linear function rule

- describe how quantities from the situation, table, or graph map to parts of the equation

**explain how transformations on a function impact its rule, table, and graph**- construct the rule of a transformed function in terms of its parent function
*Example: given f(x) = x + 3 and the table, graph, or stated transformation of g(x), write an equation of g(x) in terms of f(x)*

- describe how changing the
**coefficient**in a function rule affects its other representations*Example: if f(x) = 3x + 2 is transformed to g(x) = 6x + 2, then the rate of change between each point doubles and the steepness of the graph increases*

- create and justify the equation of a line
**parallel**to the x or y axis - determine if tables, equations, or situations modeled by two linear functions are parallel when graphed and justify reasoning

- construct the rule of a transformed function in terms of its parent function

Develop conceptual understanding with these terms:

function rule, linear equation, exponential equation, solution set, parallel, arithmetic sequence, geometric sequence, product, base, exponent, coefficient, constant

Support students in using these terms:

function, rate of change, slope, interval, input, output, domain, range, y intercept, initial value, continuous, discrete, function family