Evidence of Understanding

**identify characteristics of a function from a situation, table, graph, and equation**- describe connections between how the rate of change and initial value are represented in a situation, table or graph and its
**function rule**(emphasis on linear and exponential functions)*Example: a situation with an initial value of 4 corresponds to the point (0, 4) in the table, a y intercept at 4, f(0) = 4, and the***constant**in the function rule is 4

- analyze graphs or tables for functions in the same family with its
**parent function**rule- describe transformations from a given equation on the graph of its parent function

- strategically use a graphing calculator to verify inputs and outputs of the function
- describe advantages and disadvantages of different representations for the same function

- describe connections between how the rate of change and initial value are represented in a situation, table or graph and its

**create a table of values or graph from an explicit or recursive rule and use it to solve problems**- include function rules involving transformations, Example: g(x) = f(x) + 3 or h(x) = |x| + 4
- describe how the graph of
*any***equation**visually represents values that make the equation true - explain the relationship between
**function notation**and a specific coordinate point*Example: f(2) = 3 represents the point (2, 3) in the table or graph*- use function notation to represent coordinate points, (x, f(x)), and describe the relationship between the independent and dependent variables

- evaluate a function given a specific input or output value using the function’s graph, table, or by using the function rule to calculate the output value of a given input
*Example: evaluate f(x) = 5 by looking at the graph or table, or find f(3) by looking at the graph, table, or by calculating the value using the rule*- justify whether a given point is on a line, given the equation of the line

- justify the domain and/or range for a function rule by interpreting the situation, graph, or table of values it represents

**compare linear, quadratic, exponential and absolute value function families**- recognize similarities and differences for different function families represented in the
__same way__*Example: regardless of the function family, the initial value of always lies on the y axis, is always (0, some number) in the table, and is always the constant in the equation**Example: values in a table for linear and exponential functions are always all increasing or all decreasing while quadratic values always change direction*

- compare characteristics belonging to functions in the same family represented in
__different ways__

- recognize similarities and differences for different function families represented in the

Develop conceptual understanding with these terms:

constant, initial value, y intercept, function notation, recursive

Support students in using these terms:

function, rate of change, slope, average rate of change, interval, dependent, independent, input, output, domain, range, continuous, discrete, function family, linear, exponential, quadratic, step, and absolute value function