Further Graph Transformations and Modelling

functions year12 advanced

Further graph transformations and modelling | NSW Curriculum Website

• MAV-12-01 uses algebraic and graphical techniques to analyse trigonometric functions
• MAV-12-02 models, analyses and solves practical problems involving functions and their transformations

📖 Prior Knowledge

Content	Prerequisite relationships
Logarithms	- Define a logarithm → Interpret logarithmic scales - Apply the laws of logarithms → Apply logarithmic scales - Interpret logarithmic scales (revisited content)
Trigonometry and Measure of Angles	- Graph trig functions in radians → Transform trigonometric graphs
Trigonometric Identities and Equations	- Solve trig equations on a restricted domain → Solve transformed trig equations
Graph Transformations	- Apply combined transformations → Transform trigonometric graphs - Apply combined transformations → Model with function transformations - Describe transformations from an equation → Transform trigonometric graphs

Transformations of trigonometric functions

• Use graphing applications to explore reflections, translations and dilations of, and confirm that the principles of transformations hold for, the trigonometric functions $f(x)=\sin x$, $f(x)=\cos x$ and $f(x)=\tan x$
• Apply the principles of transformations to graph transformations of the trigonometric functions $f(x)=\sin x$, $f(x)=\cos x$ and $f(x)=\tan x$, describe which transformations have been applied to $y=f(x)$ and determine the domain, range, horizontal translation, vertical translation, dilation factor, period and amplitude when applicable
• Solve equations and graphical problems involving transformations of the trigonometric functions $f(x)=\sin x$, $f(x)=\cos x$ or $f(x)=\tan x$, using graphing applications or otherwise, within a specified domain

Modelling with functions

• Model and solve problems involving periodic phenomena using transformations of the trigonometric functions $f(x)=\sin x$, $f(x)=\cos x$ or $f(x)=\tan x$, without the use of calculus
• Model and solve practical problems involving functions and their transformations, within the scope of the Mathematics Advanced course, using graphical and algebraic techniques
• Recognise that logarithmic scales are useful to represent a variable that ranges over a large set of values and explain when a logarithmic scale is suitable
• Use logarithmic scales to model and solve problems involving decibels (dB) in acoustics, seismic scales for earthquakes, magnitudes of stars and the pH scale in chemistry