Functions, graphs, and the language of change
What students will learn
Review selected function and trigonometric prerequisites, then explain how instantaneous change arises from average rates.
Before this topic
- Algebraic manipulation
- Function notation and graph coordinates
Read and connect
Supporting reading: An Overview of Trigonometry →
Selected prerequisite review of special triangles, radians, unit-circle values, principal inverse angles, and identities. This is not complete precalculus preparation.
Supporting reading: Function Transforms →
Selected prerequisite review of reflection order, translations, scaling, inverse relations, and completing the square. This is not complete precalculus preparation.
Supporting reading: FFR (For Future Reference) →
Selected prerequisite review of domain and range restrictions, interval notation, and logarithm rules. This is not complete precalculus preparation.
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.
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.