 ## Functions

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### A1.1 Algebraic operations

This section introduces the basic skills for addition, subtraction, multiplication and division (+ - × ÷) of algebraic expressions.

### A1.3 Removing brackets

What do I do with the brackets? Brackets are useful to group numbers, pronumerals and operations together as a whole. Whatever is around the brackets affects all the things inside the brackets. View...

### A1.4 Algebraic fractions: Addition and subtraction

How do I deal with fractions involving pronumerals? Adding and subtracting fractions always requires a common denominator (which is the lower half of the fraction). These need to be the same before...

### A1.5 Algebraic fractions: Multiplication and division

What is an algebraic fraction? The numerator(top) or denominator(bottom) of a fraction can be in algebraic form involving numbers and variables (represented by pronumerals or letters). In this...

### A2.1 Rearranging formulae

Learn how to manipulate or rearrange formulas that involve fractions and brackets.

### A2.3 Transposition of formulas with challenges

Are you still trying to get that variable on its own from the formula, but it is in a tricky place – or maybe it appears more than once? Here we demonstrate manipulating or rearranging complex...

### Algebra

What is algebra? Why are there letters in the equation? Algebraic expressions involve pronumerals (letters) to represent values. Pronumerals can take many different values. We often need to plug...

### FG1 Functions and relations

A relation is a set of ordered pairs.

### FG10 (T8) Graphs of sine and cosine functions

Both the functions y = sin x and y = cos x have a domain of R and a range of [-1,1].

### FG2 Interval notation

Often the domain of a function will be restricted to a subset of R. This subset is called an interval, and the end points are a and b.

### FG3 Inverse notation

If f to the power of -1 times (x) is the inverse function of a one-to-one function f(x) then f to the power of -1 times (x) is the set of ordered pairs obtained by interchanging the first and...

### FG4 Absolute value functions

The absolute value of a number x gives a measure of its size or magnitude regardless of whether it is positive or negative. If a number is plotted on a number line then its absolute value can be...

### FG5 Hybrid functions

Functions which have different rules for each subset of the domain are called hybrid functions. Sometimes they are referred to as piecewise defined functions.

### FG6 (T6) Circular functions

The trigonometric ratios that have been defined in right-angled triangles can be extended to angles greater than 90 degrees

### FG7 Linear graphs

Understanding a linear graph is the simplest way of representing data or a functional relationship. This module explains the equations and visuals of a linear graph.

The graph of a quadratic function is called a parabola.

### FG9 Graphs and transformations

The known graphs of some simple functions and relations can be used to sketch related, but more complicated functions.

### Functions and graphs

Information about functions and graphs to improve your maths skills in these areas

### T1 Pythagoras’ theorem

Pythagoras’ Theorem shows the relationship between the sides of a right-angled triangle. Knowing the length of two sides of a right-angled triangle, the length of the third side can be calculated.

### T2 Right triangle trigonometry

Sine, cos and tan can be defined using side lengths of a right-angled triangle. These side lengths are identified as either the hypotenuse or the opposite or adjacent sides to the angle.