A function is a mathematical relationship that uniquely maps values of one set to the values of another set.

The domain of a function is the set of values that the mapping is performed on.

The range of a function is the set of values mapped to by the function and the stated domain.

Checking and securing understanding of functions

Maths

Defining function notation

Finding the inverse of a function

Writing composite functions

Solving equations involving functions

Solving equations involving composite functions

General algebraic forms for specific number properties

Making conjectures about patterns and relationships

Proving or disproving a statement

Writing a generalised statement about specific number properties

Writing a proof

Logical arguments

Multiple approaches to logical arguments

Problem solving with functions and proof

In this future unit, pupils continue to explore composite functions, thereby building on their work from this unit. Pupils need to understand function notation from this unit as this is used in iteration.

The functions unit requires pupils to write composite functions and pupils will need to draw on their understanding of how to manipulate various algebraic expressions and equations, including algebraic fractions.

In this unit pupils will further develop their understanding of algebraic notation and graphs by learning about functions, their inverses and composite functions.

Functions and proof

An inverse function reverses the mapping of the original function.

The composite function gf($$x$$) is the combination of f($$x$$) and g($$x$$). The output from f($$x$$) is the input for g($$x$$).

An equation is used to show two expressions that are equal to each other.

A multiple is the product of a number and an integer.

An integer is any positive or negative whole number or zero.

A prime number is an integer greater than one with exactly 2 factors.

A triangular number is a number that can be represented by a pattern of dots arranged into an equilateral triangle. The term number is the number of dots in a side of the triangle.

A conjecture is a (mathematical) statement that is thought to be true but has not been proved yet.

To generalise is to formulate a statement or rule that applies correctly to all relevant cases.

A rational number is one that can be written in the form a/b where a and b are integers and b is not equal to 0

An irrational number is one that cannot be written in the form a/b where a and b are integers and b is not equal to 0

The apex is the point (vertex) which is the greatest perpendicular distance from the base.

If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.

The hypotenuse is the side of a right-angle triangle which is opposite the right angle.

An expression contains one or more terms, where each term is separated by an operator.

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Functions and proof

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