Achievement objective M82
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.
Indicators
 Demonstrates understanding of inverse and/or reciprocal functions, including those of:
 polynomial
 exponential y = e^{ax} or y = b^{x}
 logarithmic
 rectangular hyperbola
 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
M86, solving equations
M87 and identification of discontinuities
M810.
 See
key mathematical ideas on NZmaths.
Progression
M82 links from M72.
Possible context elaborations
 Given the graph of e^{x}, 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 subjectspecific resources pages are very helpful. From there, you can find all the achievement standards and links to assessment resources, both internal and external.
Learn more:
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.
Refer to the
mathematics and statistics matrix.
Last updated September 26, 2013
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