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BetterGrades Precalculus · Unit 16 · Unit map

Calculus Readiness and Function Synthesis

A graph is positive, decreasing, concave upward, has domain all reals, and approaches y=2 as x grows. Name plausible families and identify one additional feature needed.

Precalculus · Unit 16

The lesson path

A graph is positive, decreasing, concave upward, has domain all reals, and approaches y=2 as x grows. Name plausible families and identify one additional feature needed.

Core sequence

Calculus Readiness and Function Synthesis

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

  1. 01Function-family classificationClassify unfamiliar formulas, graphs, tables, and contexts using structural evidence.
  2. 02Model selection and comparisonSelect and compare function models using patterns, residuals, domains, and parameter meanings.
  3. 03Average rate of change revisitedCompare average rates across function families and interpret units and interval dependence.
  4. 04Difference quotientsConstruct and simplify f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h} and interpret its components.
  5. 05Secant lines and tangent intuitionInterpret tangent slope as a limiting value of secant slopes.
  6. 06Local linearity and magnificationRecognize when a smooth graph appears linear under magnification and identify failures of local linearity.
  7. 07Intuitive limitsEstimate limits from tables, graphs, and algebra while distinguishing approached value from function value.
  8. 08Continuity and discontinuityClassify removable, jump, infinite, and endpoint discontinuities using function values and limiting behavior.
  9. 09Infinite behavior and asymptotesSynthesize finite and infinite input behavior across polynomial, rational, exponential, logarithmic, and trigonometric families.
  10. 10Numerical approximation and sensitivityUse bracketing, iteration, finite differences, and residuals while evaluating sensitivity to rounding and parameter error.
  11. 11Accumulation, finite sums, and area previewConnect rates, rectangles, finite sums, net change, and area under a rate graph.
  12. 12Precalculus synthesis capstoneAnalyze an unfamiliar multirepresentation problem by selecting and combining methods from the entire course.
Assessment path

Review, practice, demonstrate, investigate

Source record

References used for this unit

  • AP Precalculus mathematical practices
  • Lippman & Rasmussen, rates of change and function behavior
  • BetterGrades Calculus Limits and Continuity course
  • Stitz & Zeager, function synthesis and numerical methods