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BetterGrades Precalculus · Unit 2 · Unit map

Functions and Multiple Representations

An input is supplied to a relationship, an output is determined by it, and parameters remain fixed for one selected model.

Precalculus · Unit 2

The lesson path

An input is supplied to a relationship, an output is determined by it, and parameters remain fixed for one selected model.

Core sequence

Functions and Multiple Representations

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

  1. 01Quantities, variables, and dependencyIdentify the input, output, parameters, and units in a quantitative relationship and explain how the quantities depend on one another.
  2. 02Relations and functionsDetermine whether a relation is a function by applying the rule that each allowed input has exactly one output.
  3. 03Function notation, evaluation, and solvingUse function notation accurately and distinguish finding an output from finding inputs that produce a chosen output.
  4. 04Words, tables, graphs, and formulasTranslate a function relationship among verbal, tabular, graphical, and algebraic representations while preserving quantities, units, and domain.
  5. 05Domain from formulasDetermine the real domain of a function by combining denominator, even-root, logarithm, and composition restrictions.
  6. 06Domain from contextDistinguish the algebraic domain of a formula from the inputs that are meaningful in a model.
  7. 07Range and global graph behaviorRead range, intercepts, extrema, boundedness, symmetry, and intervals of increase or decrease from a graph.
  8. 08Piecewise-defined functionsEvaluate, graph, and interpret functions that use different rules on different parts of the domain.
  9. 09Average rate of changeCalculate and interpret average rate of change as output change per input change and as the slope of a secant line.
  10. 10Function representation and modeling studioConstruct, compare, and defend function representations while stating assumptions, domain, units, and limitations.
Source record

References used for this unit

  • Yoshiwara, Modeling, Functions, and Graphs
  • Lippman and Rasmussen, Precalculus Volume 1
  • Stitz and Zeager, Precalculus

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