Big Idea:

Big Idea 3

Function rules describe the quantitative relationships between variables.

1 week

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  
    • 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∙bx (base and exponent bx 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
    • 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 


  • 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  


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

Core Resource
A core resource supports multiple days of instruction. COMING SOON!
    Instructional Routine: Connecting Representations
    These tasks are embedded within the instructional routine called Connecting Representations.