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Achievement objective M8-2

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

  • display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions.


  • Demonstrates understanding of inverse and/or reciprocal functions, including those of:
    • polynomial
    • exponential y = eax or y = bx
    • logarithmic
    • rectangular hyperbola y equals a divided by bracket x plus or minus b bracket.
    • trigonometric equations of the form y = Asin(Bx ) + C for sin, cos and tan functions with x in radians or degrees
    • f(x) = √ x
  • Makes graphical and algebraic connections between a function and its inverse, including the consideration of restrictions on the domain of a function so that its inverse is also a function.
  • Makes links with manipulate trigonometric expressions M8-6, solving equations M8-7 and identification of discontinuities M8-10.
  • See key mathematical ideas on NZmaths.


M8-2 links from M7-2.

Possible context elaborations

  • Given the graph of ex, sketch its inverse function.
  • Given a function algebraically, find the rule for its inverse.
  • Explore the reciprocals and inverses of trigonometric functions.
  • Investigate families of functions and their inverses making connections between transformations of a graph and changes to the equation of the graph.
  • Use equations of functions to model situations such as temperature data, tides, ferris wheels, ski slopes, population growth.
  • Activity: Big Bang Theory - Fractals and complex numbers
  • Activity: Linking integration and differentiation

Assessment for qualifications

NCEA achievement standards at levels 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the NZQA website.

The NZQA subject-specific resources pages are very helpful. From there, you can find all the achievement standards and links to assessment resources, both internal and external.

The following achievement standard(s) could assess learning outcomes from this AO:

  • There are currently no achievement standards that could assess learning outcomes from this AO.

Last updated September 11, 2018