Evidence of Understanding

**justify why a table of values and graph are equivalent representations for the same function**- e.g., map coordinate points on a graph to specific pairs of values in a table, recognize increasing output values in the table correspond to an increasing interval on the graph, etc.
- describe when a graph may be more useful than a
**table of values**(and vice versa)

**create equivalent mathematical representations for linear, quadratic, exponential, or step functions**- analyze information from a graph or situation, represent the key features in an organized table of values, and justify why both representations are equivalent
- use
**function notation**to represent coordinate points and describe the relationship between the independent and dependent variables

- use
- create a graph that models a situation and justify its characteristics (or vice versa)
- create a situation or graph that accurately represents a function's table of values
- create graphs with a
**scale**other than 1 and use the domain and range to justify choices

- create graphs with a
- understand how to label all important parts of tables and graphs (input, output, axes, title, lines extended, etc.) and how these labels translate across equivalent representations
- e.g., the label for the axes corresponds to the units in the situation, the scale of the graph corresponds to quantity changes in the table, lines are extended according to the situation, etc.

- e.g., the label for the axes corresponds to the units in the situation, the scale of the graph corresponds to quantity changes in the table, lines are extended according to the situation, etc.

- analyze information from a graph or situation, represent the key features in an organized table of values, and justify why both representations are equivalent
**recognize functions and non-functions from tables, mappings, graphs, etc.**- identify and justify the domain and range of a function from a situation, table, or graph
- recognize when using interval or set notation is useful and efficient for representing the domain and range of a function with a large number of values

- utilize the Vertical Line Test as a visual way to determine if a given graph is a function or not
- analyze various representations and notice that functions are single-valued mappings from the domain of the function to its range and an input has
*at most*one output.

- identify and justify the domain and range of a function from a situation, table, or graph

Develop conceptual understanding:

table of values, scale, domain, range, function, relation, vertical line test, function notation, f(x)

Supporting terms to communicate:

axes, units, coordinate point, ordered pair, interval, increasing, decreasing, positive, negative, turning point, maximum, minimum, intercept, dependent, independent, domain, range, continuous, discrete, interval and set-builder notation