Study Guide — HSF.BF.A.1
Write a function that describes a relationship between two quantities
Build new functions from existing ones (transformations, composition, inverse).
What this standard means
- Determine an explicit expression, a recursive process, or steps for calculation from a context.
- Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
- (+) 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 weather balloon as a function of time.
- Apply write a function that describes a relationship between two quantities with models and explanation
_See printable PDF for diagram._
How to use the 20 practice sets
| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |
Pacing: 10–15 minutes per session.
How to practice
1. Track how transformations shift graphs 2. Compose step by step: f(g(x)) 3. Verify inverse pairs with composition
_See printable PDF for diagram._
Common mistakes
- Wrong direction of shifts
- Composition order reversed
Review and practice tests
1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for HSF.BF.A.1.
- [ ] Applies transformations to graphs
- [ ] Composes functions correctly
- [ ] Finds or verifies inverses when applicable
Materials for this standard
- Practice Problems — 20 printable sets
- Review — 10 difficulty levels
- Practice Test — 10 difficulty levels
- Answer key — for parents and tutors