Functions Toolkit (OCR GCSE Maths)

Revision Note

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Maths

Introduction to Functions

What is a function?

  • A function is a combination of one or more mathematical operations that takes a set of numbers and changes them into another set of numbers
    • It may be thought of as a mathematical “machine”
    • For example, if the function (rule) is “double the number and add 1”, the two mathematical operations are "multiply by 2 (×2)" and "add 1 (+1)"  
      • Putting 3 in to the function would give 2 × 3 + 1 = 7
      • Putting -4 in would give 2 × (-4) + 1 = -7 
    • Putting in would give x would give 2x + 1
  • The number being put into the function is often called the input
  • The number coming out of the function is often called the output
  • A function can be shown in a diagram form
    • space x space rightwards arrow space box enclose space cross times 5 space end enclose space rightwards arrow space box enclose space plus 6 space end enclose space rightwards arrow space y
      • The input is x and the output is y
      • In algebra, this says 5x + 6 = y

Worked example

A function is given by

space input space rightwards arrow space box enclose space cross times 3 space end enclose space rightwards arrow space box enclose space minus 8 space end enclose space rightwards arrow space output

(a)
If the input is 10, find the output.
  
Substitute the number 10 into the function
  
10 cross times 3 minus 8
  
Work out this value
  
The output is bold 22

(b)
If the input is k, find an algebraic expression for the output.
 
Substitute the letter k into the function
k × 3 - 8
The output is 3k - 8

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Mark

Author: Mark

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.