Common Core · High school
HSF-BF.A.1.C
High school — Compose functions; for example, if T(y) is the temperature in the atmosphere as a function of height and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the balloon as a function of time.
A note on this mapping: HSF-BF.A.1.C is a (+) standard — beyond the college- and career-ready threshold, i.e. precalculus rather than Algebra II.
The skill that covers it
What a student should be able to do
- Evaluate (f ∘ g)(a) and (g ∘ f)(a) from function rules and from tables, and explain why the order matters.
- Write f(g(x)) as a single simplified expression when the outer function is not linear.
- State the domain of a composition by tracking the restrictions of both functions.
- Decompose a function into an outer and an inner function, and model a two-stage situation with a composition.