Back to the full dot-point answer
VICMath MethodsQuick questions
Unit 3
Quick questions on Transformations, composite and inverse functions: VCE Math Methods Unit 3
13short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is order of operations?Show answer
When described in words, the conventional order is dilation, then reflection, then translation. VCAA marking guides accept any consistent order if the algebra produces the same final rule.
What is effect on key features?Show answer
For each function family, transformations move key features predictably:
What is existence condition?Show answer
For $f \circ g$ to be defined on a set $S$, the range of $g$ restricted to $S$ must be a subset of the domain of $f$. If $g$ produces outputs outside the domain of $f$, the composite is undefined there.
What is three exam patterns?Show answer
VCAA examines composites in three patterns.
What is worked example?Show answer
Let $f(x) = \sqrt{x}$ (domain $[0, \infty)$) and $g(x) = x - 4$ (domain $\mathbb{R}$).
What is finding the inverse?Show answer
1. Start with $y = f(x)$. 2. Swap $x$ and $y$: $x = f(y)$.
What is domain and range swap?Show answer
The domain of $f^{-1}$ equals the range of $f$. The range of $f^{-1}$ equals the domain of $f$.
What is graphical property?Show answer
The graph of $f^{-1}$ is the reflection of the graph of $f$ in the line $y = x$. So if $f$ has y-intercept at $(0, c)$, then $f^{-1}$ has x-intercept at $(c, 0)$.
What is transformation order confusion?Show answer
"Translate then dilate" produces a different result than "dilate then translate" when described in words. Always rewrite into the standard form $A f(n(x - b)) + c$ and identify the four parameters first.
What is forgetting the reciprocal in horizontal dilation?Show answer
$n = 3$ compresses by factor $\frac{1}{3}$, not $3$.
What is skipping the existence condition for composites?Show answer
Writing $f \circ g(x) = \sqrt{x - 4}$ without stating that $x \geq 4$ loses a domain mark.
What is inverting a non-one-to-one function without restricting the domain?Show answer
$f(x) = x^2$ on $\mathbb{R}$ has no inverse. You must restrict (e.g. to $x \geq 0$) before swapping.
What is forgetting that domain and range swap for the inverse?Show answer
Markers expect both stated explicitly.