Mathematical Methods Unit 1
Sample context for assessment – features of graphs of
functions from data
Introduction
This short task has two parts, both based on identification of features of graphs of functions. The
functions involved represent real life data and are not specified by a rule. Students are asked to
use the graph to identify:




domain, range and codomain for the function
points corresponding approximately to local and global maxima and minima, where there is
sudden change, where the function has a specified value
approximate intervals corresponding to subsets of the domain over which the function is
steady, increasing, decreasing, above, below or between specified values
other features of the function
Part 1
Consider the function represented by the following smoothed trend graph which shows the
Australian-US exchange rate (Australian dollar in terms of US dollar) for about a month (source:
http://www.ozforex.com.au/forex-tools/my-fx-dashboard ).
1.
2.
3.
4.
5.
6.
7.
8.
State the domain and range and a suitable codomain.
State the coordinates of any local maximum or minimum values.
State the coordinates of the global maximum and the global minimum.
Find when the Australian dollar was worth 0.77 US
State intervals over which the Australian dollar was steady, increasing or decreasing in value
with respect to the US dollar
Find the intervals during which the Australian dollar was between 0.77 US and 0.78 US
Find the intervals during which the Australian dollar was above 0.80 US
Find the intervals during which the Australian dollar was below 0.77 US
Part 2
Obtain a graph of similar data for a function that represents some other context, such as
temperature, rainfall, pollution level, water levels, heartbeat or blood pressure.
Analyse the graph of the function as in Part 1 and note any other features of the graph, such as
point of sudden change, cycles, symmetry or asymptotic behaviour.
© VCAA
Mathematical Methods Unit 1
Areas of study
The following content from the areas of study is addressed through this task.
Unit 1
Area of study
Content dot point
Functions and graphs
2, 4
Algebra
8
Calculus
2
Probability and statistics
-
Outcomes
The following outcomes, key knowledge and key skills are addressed through this task.
Unit 1
Outcome
Key knowledge dot point
Key skill dot point
1
3
2
2
1, 2
2, 4, 5
3
1, 2
3, 5, 10
© VCAA
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