NY Next Generation Math AII-F.BF.1.b

MathGrades 9–12Write a function that describes a relationship between two quantities.

The Standard

Combine standard function types using arithmetic operations.

New York State Next Generation Mathematics Learning Standards · Build a function that models a relationship between two quantities.

Teacher's field guide

What Students Need to Do: Students combine familiar Algebra II function types through addition, subtraction, multiplication, or division. They interpret how the operation creates a new relationship and domain.
What Mastery Looks Like: The student writes the combined rule, simplifies where useful, and determines domain restrictions from both component functions and the operation. Input-output checks confirm the result.
Common Misconceptions: Students may combine outputs without applying the operation to full expressions or ignore zeros in a denominator. They may confuse function composition with arithmetic combination.
How to Assess It: Let f(x) equal x squared plus 1 and g(x) equal x minus 2. Ask for f divided by g, its domain, and its value at x equals 3.

Lesson moves

Join function-machine cards with operation cards and track one input through both machines to a combined output.
Ask students how division changes the domain of two otherwise unrestricted functions.
Play combine and check by matching component functions, operations, resulting rules, and domain restrictions.
Combine revenue and cost functions to model profit, or distance and time functions to model a rate.

Free download

$Preview of the AII-F.BF.1.b printable worksheet$

A ready-to-print activity worksheet aligned to AII-F.BF.1.b, with an answer key for the teacher on its own page. No account needed.

PDF, US Letter, prints cleanly in black and white.

Keep exploring

Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.