Support · Mathematics Extension 1 11–12 – Year 11 · Further work with functions

Support Examine the relationship between the graph of y = f(x) and the graphs of y = |f(x)| and y = f(|x|) using graphing applications, and graph y = |f(x)| and y = f(|x|) given y = f(x) in algebraic or graphical form

Resources for the prerequisite content of this dot point: earlier-stage (or earlier sub-level) dot points in the same strand that students usually need first. Use these to fill gaps before or alongside the core lesson.

Prerequisite links are draft mappings generated from the syllabus structure (earlier stage, same strand, closest content). They are being reviewed by teachers. Spot a poor match? Tell us.

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Prerequisite dot points

Use graphing applications to graph and compare functions of the form y = f(x),y = f(x) + c, y = f(x - b), y = kf(x) and y = f(ax), and describe their transformations

Stage 5 · Functions and other graphs (Path) Draft mapping

  • Interactive toolStarterEnrichment
    Desmos Graphing Calculator
    Desmos · Interactive (browser) · Free · Link checked 2026-10-15 · No prep
    Use it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
  • Interactive toolEnrichment
    GeoGebra Classic
    GeoGebra · Interactive (browser) · Free · Link checked 2026-10-15 · No prep
    Use it for: Dynamic geometry and graphing for constructions and proofs.

Graph the function Q = Ae^(kt), where k > 0 and k and A > 0 and A, with and without graphing applications, and identify any asymptotes

Mathematics Advanced 11–12 – Year 12 · Applications of calculus Draft mapping

  • Interactive toolStarterEnrichment
    Desmos Graphing Calculator
    Desmos · Interactive (browser) · Free · Link checked 2026-10-15 · No prep
    Use it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
  • Interactive toolEnrichment
    GeoGebra Classic
    GeoGebra · Interactive (browser) · Free · Link checked 2026-10-15 · No prep
    Use it for: Dynamic geometry and graphing for constructions and proofs.

Solve equations and graphical problems involving transformations of the trigonometric functions f(x) = sin⁡x, f(x) = cos⁡x or f(x) = tan⁡x, using graphing applications or otherwise, within a specified domain

Mathematics Advanced 11–12 – Year 12 · Further graph transformations and modelling Draft mapping

  • Interactive toolStarterEnrichment
    Desmos Graphing Calculator
    Desmos · Interactive (browser) · Free · Link checked 2026-10-15 · No prep
    Use it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
  • Interactive toolEnrichment
    GeoGebra Classic
    GeoGebra · Interactive (browser) · Free · Link checked 2026-10-15 · No prep
    Use it for: Dynamic geometry and graphing for constructions and proofs.