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

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

When graphing functions the $$x$$ values are the domain and the $$y$$ values are the {{}}.

None of these values belong only to the range.

Which of these values belong to the range, but not the domain, of the function $$x^2+5$$?

All of these values will be in the range of the function $$5-x^2$$

Which of these values belong to the domain, but not the range, of the function $$5-x^2$$?

On which of the below would we need to restrict the domain in order to make the function valid?

Which of these are many-to-one functions?

When graphing the linear equation $$y=5x-8$$ what is the value of the $$y$$ coordinate when $$x=3$$?

When graphing the linear equation $$y=5x-8$$ what is the value of the $$y$$ coordinate when $$x=-1$$?

When we graph the equation $$y=8 - x^2$$ what is the maximum value (i.e. the largest value of the $$y$$ coordinate)?

$$x=7$$ is not a valid input for which of these equations?

Which $$x$$ values cannot be input into the equation $$y={x+2\over{(x-3)(x+5)}}$$?

Checking and securing understanding of functions

Lesson outcome