Functions, graphs, and the language of change
What students will learn
Explain how instantaneous change arises from average rates; use selected prerequisite review as needed before beginning the native BC path.
Before this topic
- Algebraic manipulation
- Function notation and graph coordinates
Read and connect
Read: Introducing Calculus: Can Change Occur at an Instant? →
Explain instantaneous change as a limit of average rates, keeping amount and rate units separate.
Check understanding
Use the complete prompt to make student reasoning visible, then consult the separate worked reasoning and criteria. A reading completion tick records reading history.
Explain a cart’s instantaneous rate →
Form and simplify a variable-interval rate, then take its limit with motion units.
Checks instantaneous change; it does not assess the whole prerequisite review.
Supporting readings and further study
- Review unit-circle angles and trigonometry →
Selected prerequisite review of special triangles, radians, unit-circle values, principal inverse angles, and identities.
Optional retained AB source reading outside the BC sequence. Selected prerequisite review, not complete precalculus preparation.
- Review function transformations →
Selected prerequisite review of reflection order, translations, scaling, inverse relations, and completing the square.
Optional retained AB source reading outside the BC sequence. Selected prerequisite review, not complete precalculus preparation.
- Review domains, ranges, and logarithms →
Selected prerequisite review of domain and range restrictions, interval notation, and logarithm rules.
Optional retained AB source reading outside the BC sequence. Selected prerequisite review, not complete precalculus preparation.
Standards and earlier reading lists
These topic placements organize reading. Edition-qualified Standards mappings and the existing complete unit task sets retain their reviewed scope.