CCSS.Math.Content.HSF-BF.A.1c
The Standard
(+) Compose functions.
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 connect two functions so the output of one becomes the input of the other. They write, evaluate, and interpret compositions in symbols and context.
What Mastery Looks Like
- Students correctly substitute one function into another and simplify the result. They explain the order of composition and identify inputs for which the composition is defined.
Common Misconceptions
- Students often reverse the order and treat f(g(x)) as g(f(x)). They may also multiply the functions, combine unlike terms, or ignore input restrictions.
How to Assess It
- Give f(x) = 2x + 3 and g(x) = x². Ask students to find f(g(x)), g(f(x)), and each value when x = 2.
Lesson moves
Ways to Teach It
Use labeled input and output cards to build two function machines, then pass values through both machines in different orders.
Ask students to explain in writing why f(g(x)) and g(f(x)) usually give different results.
Run a matching game with cards showing function pairs, compositions, simplified expressions, and evaluated outputs.
Model a weather balloon by composing height over time with temperature by height, then interpret the units of the result.
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Printable HSF-BF.A.1c Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSF-BF.A.1c, with an answer key for the teacher on its own page. No account needed.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSF-IF.A.2
Composing functions requires using notation like f(g(x)) and treating one function’s output as another function’s input.
- CCSS.Math.Content.HSF-IF.A.1
Composing functions requires knowing that f(x) is an output for an input and can become another function’s input.
- CCSS.Math.Content.HSA-SSE.A.1b
Composing functions requires treating the inner function or expression as one input when substituting into the outer rule.
What This Unlocks
Mastery here sets students up for these next.
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Related Standards
- CCSS.Math.Content.HSN-VM.B.4
(+) Add and subtract vectors.
- CCSS.Math.Content.HSS-CP.B.9
(+) Use permutations and combinations to compute probabilities of compound events and solve problems.
- CCSS.Math.Content.HSN-CN.B.5
(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representatio...
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