CCSS.Math.Content.HSF-BF.A.1b
The Standard
Combine standard function types using arithmetic operations.
Common Core State Standards for Mathematics · Build a function that models a relationship between two quantities
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students represent each part of a situation with a familiar function, such as constant, linear, quadratic, or exponential. They combine the outputs using arithmetic and explain what each part contributes.
What Mastery Looks Like
- Students can write one function that combines two or more familiar function types. They can explain what each part represents and use the model to calculate or predict a value.
Common Misconceptions
- Students may confuse adding functions with composing them, writing f(g(x)) instead of f(x) + g(x). They may ignore units, domain limits, or the meaning of each term.
How to Assess It
- Give this exit ticket: A room is 20°C, and coffee starts 60°C above room temperature, with the difference halving every 10 minutes. Write T(t), label both parts, and find T(20).
Lesson moves
Ways to Teach It
Measure warm water and room temperature, then model water temperature as room temperature plus a decaying temperature difference.
Explain in writing how f(x) + g(x) differs from f(g(x)), using a numerical example.
Run a card sort matching situations, component functions, combined formulas, and graphs.
Model a taxi fare by adding a fixed starting fee to a linear charge based on distance.
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Printable HSF-BF.A.1b Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSF-BF.A.1b, 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 worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSF-IF.A.1
Combining functions by arithmetic requires knowing function notation, inputs, outputs, and that each resulting rule still defines outputs from a domain.
- CCSS.Math.Content.HSF-IF.A.2
Students use function notation and evaluation to define and interpret sums, differences, products, or quotients of functions.
- CCSS.Math.Content.7.EE.A.1
Adding, multiplying, and simplifying algebraic expressions carries over when forming formulas like f(x)+g(x) or f(x)g(x).
Keep exploring
Related Standards
- CCSS.Math.Content.HSA-APR.A
Perform arithmetic operations on polynomials
- CCSS.Math.Content.6.EE.A.2a
Write expressions that record operations with numbers and with letters standing for numbers.
- CCSS.Math.Content.1.OA.B.3
Apply properties of operations as strategies to add and subtract.
- CCSS.Math.Content.HSN-CN.A
Perform arithmetic operations with complex numbers.
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