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.

Defining function notation

Maths

Checking and securing understanding of functions

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

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

Instead of writing 'the function $$5x-8$$' we would write it using the shorthand notation ...

If $${\text{f}}(x)=12-5x$$ then $${\text{f}}(3)=$${{}}.

If $${\text{f}}(x)=12-5x$$ evaluate $${\text{f}}(-2)$$.

If $${\text{f}}(x)=5x+12$$ evaluate $$7{\text{f}}(4)$$ {{}}

If $${\text{f}}(x)=5x+12$$ and $${\text{g}}(x)=2-3x$$ evaluate $${\text{f}}(4)-{\text{g}}(3)$$ {{}}

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

$$x$$ is multiplied by $$3$$ then $$7$$ is added.

$$7$$ is added to $$x$$ then the sum is multiplied by $$3$$

$$x$$ is multiplied by $$3$$ then $$7$$ subtracted

$$x$$ is multiplied by $$3$$ then subtracted from $$7$$

$$x$$ is subtracted from $$3$$, then the result is multiplied by $$7$$

$$3$$ is subtracted from $$x$$, then the result is multiplied by $$7$$

Match the expression to the description of each function.

When graphing the linear equation $$y=7x+9$$ what is the value of the $$y$$ coordinate when $$x=5$$?

When graphing the linear equation $$y=7x+9$$ what is the value of the $$y$$ coordinate when $$x=-5$$?

When graphing the equation $$y=10-x^2$$ what is the value of the $$y$$ coordinate when $$x=-3$$?

Which of the below are invalid inputs into the equation $$6\over{x^2+x-20}$$?

Starter Quiz

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