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VCE Math Methods Unit 1 AOS 2
Relations & Functions
A function is a special type of relation where every input has exactly one unique output. This is checked graphically using the vertical line test. Click the cards to explore the key concepts of Domain and Range.
Domain
The set of all possible x-values for which a function is defined.
The maximal (or implied) domain is the largest possible set of inputs a function can have. For f(x) = \sqrt{x-2}, the expression under the root must be non-negative, so the maximal domain is [2, \infty).
Range
The set of all actual y-values that a function produces.
The range depends on the function’s rule and its domain. For f(x) = \sqrt{x-2}, the output is always non-negative, so the range is [0, \infty).
Systematic Polynomial Factorisation
Factorising polynomials is a key skill for solving equations. It’s not guesswork; it’s an algorithm based on the Remainder and Factor Theorems. Click through the steps below to see the process for factorising P(x) = x^3 – 7x + 6.
Transformations of Functions
Understanding how parameters a, n, h, and k affect a function’s graph is crucial. Use the sliders to explore their effect on the base function y=x^2.
Description of Transformations:
Inverse Functions
An inverse function f^{-1}(x) only exists if the original function is one-to-one (passes the horizontal line test). For many-to-one functions, we must first restrict the domain.
Exploring the Inverse of f(x) = (x-1)^2
The function is many-to-one. Restrict the domain to find an inverse.
Systems of Simultaneous Equations
Solving a system of two linear equations corresponds to finding the point of intersection of their graphs. There are three possible outcomes. Click the buttons to visualize each case.
