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      Defining function notation

      Lesson details

      Learning outcome

      I can define function notation.

      Key learning points

      1. There is a shorthand for writing a function.
      2. The notation means that the whole function does not need to be written out each time.
      3. The notation should always be defined at the start.
      4. It is possible to substitute the notation for the function it represents.

      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.

      Teacher tip

      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.

      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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      Prior knowledge starter quiz

      6 Questions

      Q1.
      A function is a mathematical relationship that uniquely __________ values of one set to the values of another set.

      Correct answer: maps
      transfers
      substitutes
      ages

      Q2.
      Match the expression to the description of each function.

      Correct Answer:$$3x+7$$,$$x$$ is multiplied by $$3$$ then $$7$$ is added.

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

      Correct Answer:$$3(x+7)$$,$$7$$ is added to $$x$$ then the sum is multiplied by $$3$$

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

      Correct Answer:$$3x-7$$,$$x$$ is multiplied by $$3$$ then $$7$$ subtracted

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

      Correct Answer:$$7-3x$$,$$x$$ is multiplied by $$3$$ then subtracted from $$7$$

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

      Correct Answer:$$7(3-x)$$,$$x$$ is subtracted from $$3$$, then the result is multiplied by $$7$$

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

      Correct Answer:$$7(x-3)$$,$$3$$ is subtracted from $$x$$, then the result is multiplied by $$7$$

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

      Q3.
      When graphing the linear equation $$y=7x+9$$ what is the value of the $$y$$ coordinate when $$x=5$$?

      Correct Answer: 44, y=44

      Q4.
      When graphing the linear equation $$y=7x+9$$ what is the value of the $$y$$ coordinate when $$x=-5$$?

      $$44$$
      $$26$$
      Correct answer: $$-26$$
      $$-44$$

      Q5.
      When graphing the equation $$y=10-x^2$$ what is the value of the $$y$$ coordinate when $$x=-3$$?

      $$19$$
      Correct answer: $$1$$
      $$-1$$
      $$-19$$
      $$-13$$

      Q6.
      Which of the below are invalid inputs into the equation $$6\over{x^2+x-20}$$?

      $$x=20$$
      $$x=0$$
      $$x=-1$$
      Correct answer: $$x=4$$
      Correct answer: $$x=-5$$

      6 Questions

      Q1.
      The __________ of a function is the set of values mapped to by the function and the stated domain.

      output
      Correct answer: range
      domain
      input

      Q2.
      Instead of writing 'the function $$5x-8$$' we would write it using the shorthand notation ...

      $$5{\text{f}}(x)-8$$
      $${\text{f}}=5x-8$$
      $${\text{f}}x=5x-8$$
      Correct answer: $${\text{f}}(x)=5x-8$$
      $${\text{f}}(x)+5x-8$$

      Q3.
      If $${\text{f}}(x)=12-5x$$ then $${\text{f}}(3)=$$ .

      Correct Answer: -3

      Q4.
      If $${\text{f}}(x)=12-5x$$ evaluate $${\text{f}}(-2)$$.

      Correct answer: $$22$$
      $$2$$
      $$-2$$
      $$-22$$

      Q5.
      If $${\text{f}}(x)=5x+12$$ evaluate $$7{\text{f}}(4)$$

      Correct Answer: 224, 7f(4)=224

      Q6.
      If $${\text{f}}(x)=5x+12$$ and $${\text{g}}(x)=2-3x$$ evaluate $${\text{f}}(4)-{\text{g}}(3)$$

      Correct Answer: 39, f(4)-g(3)=39

      To help you plan your 11 maths lesson on: Defining function notation, download all teaching resources for free and adapt to suit your pupils' needs...