Florida B.E.S.T. MA.912.F.3.2
The Standard
Given a mathematical or real-world context, combine two or more functions, limited to linear, quadratic, exponential and polynomial, using arithmetic operations. When appropriate, include domain restrictions for the new function.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students translate a situation into separate function rules, then calculate a sum, difference, product, or quotient of those rules. They simplify the result and remove inputs barred by a denominator or the situation.
What Mastery Looks Like
- A student can keep each function grouped, perform the chosen operation, and simplify accurately. The student states restrictions from original domains, zero denominators, and the situation.
Common Misconceptions
- Some students confuse a product, f(x)g(x), with composition, f(g(x)). Others lose signs when subtracting grouped expressions. They may cancel a factor and forget that the original denominator still excludes an input.
How to Assess It
- Exit ticket: Let f(x) = x² − 9 and g(x) = x − 3. Find and simplify (f/g)(x), then state the domain and explain the excluded value.
Lesson moves
Ways to Teach It
Give pairs of function-rule cards; students draw an operation card, combine the rules on whiteboards, and attach a sticky note listing excluded inputs.
Students write an example showing how multiplying f(x) and g(x) differs from finding f(g(x)), then compare responses with a partner.
Run a matching game with cards showing function pairs, operations, simplified results, and domains; teams assemble correct four-card sets.
Model profit by subtracting a quadratic cost function from a linear revenue function, then identify input values that make sense for production.
Free download
Printable MA.912.F.3.2 Worksheet
A ready-to-print activity worksheet aligned to MA.912.F.3.2, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetKeep exploring
Related Standards
- MA.912.F.3.3
Solve mathematical and real-world problems involving functions that have been combined using arithmetic operations.
- MA.912.AR.1.6
Solve mathematical and real-world problems involving addition, subtraction, multiplication or division of polynomials.
- MA.912.F.3.1
Given a mathematical or real-world context, combine two functions, limited to linear and quadratic, using arithmetic operations. When appropriate, include domai...
- MA.912.F.3.5
Solve mathematical and real-world problems involving composite functions.
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.