9 Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
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Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Big Idea:

### 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
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