Big Idea:

Big Idea 2

Functions can be represented in multiple, equivalent ways.

1 week

Evidence of Understanding

  • compare a table of values with a situation or graph that models it
    • identify and describe how key features of a graph are represented in a table of values
      • Example: 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)
    • interpret domain and range values in a table within the context of a situation

 

  • 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, (x, f(x)), and describe the relationship between the independent and dependent variables
    • 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

 

  • recognize functions and non-functions from tables, mappings, graphs, or situations
    • identify and justify the domain and range of a function from a situation, table, or graph
      • explore and justify when interval or set notation is useful for representing the domain and range
    • use the Vertical Line Test as a visual tool to determine if a given graph is a function or relation
    • 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

 

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

Core Resources
  • Interpreting Information
    Multiple-day resource that helps students interpret and make deeper sense of intercepts, mins, maxs, domain, range, and other key information from multiple representations.
    Resource:
    Interpreting Information

    Multiple-day resource that helps students interpret and make deeper sense of intercepts, mins, maxs, domain, range, and other key information from multiple representations.

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