NY Next Generation Math AII-F.BF.1

AII-F.BF.1 is a cluster heading. These are the individual standards under it.

• AII-F.BF.1.a

  Determine a function from context. Determine an explicit expression, a recursive process, or steps for calculation from a context.

• AII-F.BF.1.b

  Combine standard function types using arithmetic operations.

01

What Students Need to Do

Students build Algebra II functions that describe relationships between quantities. They choose suitable linear, quadratic, exponential, recursive, or combined function structures from context.

02

What Mastery Looks Like

The student defines inputs and outputs, selects a fitting function type, and writes a rule that matches stated conditions. Values, units, and behavior confirm the model.

03

Common Misconceptions

Students may choose a function family from surface words rather than the pattern of change or omit an initial condition. They may combine functions without interpreting the new output.

04

How to Assess It

Give a cooling context with an ambient temperature and exponential decay. Ask students to define quantities and write a function combining the constant and decay components.

1. 01

   Arrange context, quantity, change-pattern, and function-family cards into a model plan.

2. 02

   Ask students why a chosen function structure fits the relationship better than another family.

3. 03

   Play function builder by combining condition cards into explicit, recursive, or arithmetic-operation rules.

4. 04

   Model cooling, finance, population, or production using a function suited to the quantities' relationship.

• NY-8.F.4

  Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of...

• AII-F.IF.8

  Write a function in different but equivalent forms to reveal and explain different properties of the function.

• NY-8.F.5

  Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a funct...