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BetterGrades Precalculus · Unit 3 · Unit map

Transformations and Function Operations

A parent function is a convenient reference member identified by domain, range, symmetry, endpoints, asymptotes, and rate patterns.

Precalculus · Unit 3

The lesson path

A parent function is a convenient reference member identified by domain, range, symmetry, endpoints, asymptotes, and rate patterns.

Core sequence

Transformations and Function Operations

Move in order or enter at the exact skill you need.

  1. 01Parent-function atlasRecognize benchmark function families by domain, range, symmetry, intercepts, end behavior, and rate patterns.
  2. 02Coordinate mappings and transformation logicDerive graph transformations by tracking how input-output pairs move.
  3. 03Vertical translationsAnalyze how adding a constant outside a function changes outputs, range, intercepts, extrema, and asymptotes.
  4. 04Horizontal translationsAnalyze how replacing xx by x-h changes input locations, domain, intercepts, extrema, and vertical asymptotes.
  5. 05Reflections and symmetryReflect function graphs across coordinate axes and connect reflection rules with even and odd symmetry.
  6. 06Vertical and horizontal scalingDistinguish output scaling from input scaling and determine the resulting stretches, compressions, domains, and ranges.
  7. 07Combined transformationsAnalyze and graph functions with several transformations by tracking inputs, outputs, and key features.
  8. 08Sums and differences of functionsAdd and subtract functions pointwise, determine the common domain, and interpret combined outputs.
  9. 09Products and quotients of functionsMultiply and divide functions pointwise while analyzing zeros, restrictions, and combined graph behavior.
  10. 10Reconstructing formulas from transformed graphsUse parent-family features, transformations, and one or more data points to construct and verify a function formula.
Assessment path

Review, practice, demonstrate, investigate

Source record

References used for this unit

  • Lippman and Rasmussen, Precalculus Volume 1
  • Utah College Algebra
  • Stitz and Zeager, Precalculus