Study Guide — HSF.BF.B.3
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x…
Build new functions from existing ones (transformations, composition, inverse).
What this standard means
- Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
- Apply identify the effect on the graph of replacing f(x) by f(x) + k, k f(x… 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.B.3.
- [ ] 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