← Maths Advanced syllabus

NSWMaths Advanced

Year 12: Functions

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do we sketch graphs built from sums, differences, products, quotients and reciprocals of standard functions?

Sketch graphs of sums, differences, products, quotients, squares and reciprocals of two known functions
A focused answer to the HSC Maths Advanced dot point on combining functions graphically. How to build sketches of $f + g$, $f g$, $f / g$, $1 / f$ and $f^2$ from the graphs of $f$ and $g$, where features come from, and what asymptotes and zeros do, with worked examples.
9 min answer →

What are the key features of exponential and logarithmic graphs, and how do transformations and the inverse relationship link them?

Sketch and interpret graphs of exponential and logarithmic functions, including transformations, and use the inverse relationship between them
A focused answer to the HSC Maths Advanced dot point on exponential and logarithmic graphs. Key features of $e^x$ and $\ln x$, their inverse relationship, transformations, asymptotes, and graphs of related forms such as $e^{-x}$ and $\ln(x + a)$, with worked examples.
8 min answer →

When does a function have an inverse, and how do we form, evaluate and graph composite and inverse functions?

Form composite functions, determine when a function has an inverse, find and graph the inverse, and use restriction of domain to invert non-one-to-one functions
A focused answer to the HSC Maths Advanced dot point on composite and inverse functions. Composition order and domain, the horizontal line test, finding the inverse by swapping and solving, the reflection in $y = x$, and restricting domains to invert non-one-to-one functions, with worked examples.
9 min answer →

How do translations, reflections and dilations transform the graph of a function in a predictable way?

Apply translations, reflections and dilations to the graph of a function and identify the resulting equation
A focused answer to the HSC Maths Advanced dot point on graph transformations. Vertical and horizontal translations, reflections in the axes, vertical and horizontal dilations, the order of combined transformations, and how each affects the equation, with worked examples.
9 min answer →