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VCE Math Methods Unit 1 AOS 1
The Language of Functions
This section covers the essential definitions that distinguish functions from relations. A relation is any set of ordered pairs, while a function is a special relation where each input has exactly one output.
Graphical Tests
We use two key visual tests to classify graphs. Use the toggle to switch between them.
Vertical Line Test
This test determines if a graph is a function. If you can draw a vertical line that intersects the graph more than once, it is not a function because one x-value corresponds to multiple y-values.
Polynomial Functions
Polynomials are a core part of Methods. Use the controls below to explore how the parameters in their equations affect the graph’s shape and position. This interactive tool covers quadratics and cubics.
Other Common Graphs
This section explores key non-polynomial functions and relations. Note the importance of asymptotes for hyperbolas and the truncus, and the endpoint for the square root graph.
Graph Transformations
Transformations generate entire families of graphs from a single parent function. The standard sequence to apply them is Dilations, Reflections, then Translations (DRT). Explore the effects on y = x2 below.
Transforming base function f(x) = x^2 using y = a * f(b(x - h)) + k
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Inverse Functions
An inverse function, f-1(x), reverses the mapping of a function f(x). It only exists if f(x) is one-to-one. Graphically, f-1(x) is a reflection of f(x) in the line y=x. Use the button to see this in action for f(x) = √x.
Base function: f(x) = √x, for x ≥ 0. This is one-to-one.
Domain and Range Swap
The domain of f(x) becomes the range of f-1(x), and the range of f(x) becomes the domain of f-1(x).
- f(x) = √x: Domain is [0, ∞), Range is [0, ∞).
- f-1(x) = x2: Domain is [0, ∞), Range is [0, ∞).
