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BetterGrades Precalculus · Unit 4 · Unit map

Composition, Inverses, and Modeling

Composition represents an ordered chain in which the inner function acts first.

Precalculus · Unit 4

The lesson path

Composition represents an ordered chain in which the inner function acts first.

Core sequence

Composition, Inverses, and Modeling

Move in order when the material is new, or enter at the exact skill you need.

  1. 01Composition as sequential processingInterpret ff composed with gg as applying gg first and then f, and explain why order generally matters.
  2. 02Composition from formulasEvaluate and simplify composite functions symbolically while preserving grouping and domain conditions.
  3. 03Composition from tables and graphsEvaluate composite functions when one or both functions are represented numerically or graphically.
  4. 04Domains of composite functionsDetermine the domain of a composite by enforcing both inner-function and outer-input conditions.
  5. 05One-to-one functionsDetermine whether a function is one-to-one and explain why one-to-one behavior is required for an inverse function.
  6. 06Constructing inverse functionsConstruct an inverse function algebraically and state the swapped domain and range.
  7. 07Graphs and verification of inversesVerify inverse functions using composition and graph symmetry across y=xy=x.
  8. 08Domain restrictions and radical inversesRestrict power functions to one-to-one branches and connect those branches to principal radical functions.
  9. 09Model construction and validationBuild a multi-stage function model, state its domain and assumptions, and evaluate whether an inverse interpretation is meaningful.
Source record

References used for this unit

  • Lippman and Rasmussen, Precalculus Volume 1
  • Utah College Algebra
  • AP Precalculus framework

The learner copy is original BetterGrades material informed by these rights-separated references; no long source passage is reproduced.