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Year 11
Higher

Checking and securing understanding of functions

I can appreciate that a function is a mathematical relationship that uniquely maps a set of numbers onto another set of numbers.

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Year 11
Higher

Checking and securing understanding of functions

I can appreciate that a function is a mathematical relationship that uniquely maps a set of numbers onto another set of numbers.

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Lesson details

Key learning points

  1. A function has a set of inputs and outputs.
  2. For any valid input, there is an output.
  3. A function takes an input and performs a series of operations, leading to an output.
  4. The set of inputs is called the domain.
  5. The set of outputs is called the range.

Keywords

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

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

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

Common misconception

Pupils may confuse the domain and the range.

Drawing the graph of the function and labelling the axes correctly will help pupils connect domain and range.


To help you plan your year 11 maths lesson on: Checking and securing understanding of functions, download all teaching resources for free and adapt to suit your pupils' needs...

If pupils are struggling to know whether a relationship is a valid function, encourage them to draw the graph as the visual representation can help.
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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
$$4(x-8) - x + 3$$ is an example of...
Correct answer: an expression.
an equation.
an algebraic equation.
an algebraic term.
Q2.
When graphing the linear equation $$y=5x-8$$ what is the value of the $$y$$ coordinate when $$x=3$$?
Correct Answer: 7, y=7
Q3.
When graphing the linear equation $$y=5x-8$$ what is the value of the $$y$$ coordinate when $$x=-1$$?
$$3$$
$$13$$
Correct answer: $$-13$$
$$-3$$
Q4.
When we graph the equation $$y=8 - x^2$$ what is the maximum value (i.e. the largest value of the $$y$$ coordinate)?
Correct answer: $$8$$
$$2$$
$$0$$
$$-2$$
$$-8$$
Q5.
$$x=7$$ is not a valid input for which of these equations?
$$y={3\over7x}$$
$$y={3\over{x+7}}$$
Correct answer: $$y={3\over{x-7}}$$
$$y={x-7\over{3}}$$
Correct answer: $$y={3\over{4(x-7)}}$$
Q6.
Which $$x$$ values cannot be input into the equation $$y={x+2\over{(x-3)(x+5)}}$$?
$$-2$$
$$-3$$
Correct answer: $$-5$$
Correct answer: $$3$$
$$5$$

Exit quiz

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6 Questions

Q1.
__________ is a mathematical relationship that uniquely maps values of one set to the values of another set.
An equation
Correct answer: A function
An expression
An algebraic term
Q2.
When graphing functions the $$x$$ values are the domain and the $$y$$ values are the .
Correct Answer: range
Q3.
Which of these values belong to the range, but not the domain, of the function $$x^2+5$$?
$$5$$
$$-5$$
$$25$$
$$-25$$
Correct answer: None of these values belong only to the range.
Q4.
Which of these values belong to the domain, but not the range, of the function $$5-x^2$$?
$$5$$
$$-5$$
Correct answer: $$25$$
$$-25$$
All of these values will be in the range of the function $$5-x^2$$
Q5.
On which of the below would we need to restrict the domain in order to make the function valid?
$$y=-9x$$
Correct answer: $$y={9\over{x}}$$
$$y=-{x\over{9}}$$
Correct answer: $$y={1\over{(x+9)}}$$
Q6.
Which of these are many-to-one functions?
$$y=4x$$
Correct answer: $$y=4x^2$$
$$y=4x^3$$
Correct answer: $$y=4x^3+4x^2$$
Correct answer: $$y=4x^3-4x^2$$