Big Idea:

Big Idea 2

Functions can be represented in multiple, equivalent ways.

1 week

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

 

  • 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

 

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

Core Resource
A core resource supports multiple days of instruction.
  • Connecting Sequences to Equations
    A single day resource that helps students make connections between different representations of linear sequences.
    Resource:
    Connecting Sequences to Equations

    Students will look for connections between linear equations and visual sequences in order to learn how to chunk visual sequences and linear equations into parts that grow and parts that do not change. This involves one pair of students manipulating an interactive applet while other students watch and make their own connections with a partner.

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