Study Guide — HSF.BF.A.2

Write arithmetic and geometric sequences both recursively and with an…

Build new functions from existing ones (transformations, composition, inverse).

What this standard means

• Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*
• Apply write arithmetic and geometric sequences both recursively and with an… with models and explanation
• Applies transformations to graphs

_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.2.

• [ ] 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