Introduction Aqa Foundation

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

• The number being put into the function is often called the input

• The number coming out of the function is often called the output

What is a function machine?

• A function machine (often called a number machine) is a way of showing a function in a diagram

  • A function machine starts with an input that leads into a series of boxes each labelled with a single mathematical function

    • The number of labelled boxes is the same as the number of individual mathematical operations in the function

  • An arrow leading out of the final box gives the output of the function

How will I be expected to use functions?

• You will need to be able to use function machines to

  • Generate an output from a given input

    • Starting from the left hand side, apply the mathematical operation in the first box to the given input

    • Apply the mathematical operation in the next box to the result

    • Write down the output value after all operations have been completed

  • Find an input from a given output

    • Redraw the function machine with the opposite mathematical operations in the boxes and the arrows pointing in the other direction

    • Starting from the right hand side, apply the opposite mathematical operation to the given output

    • Apply the opposite mathematical operation in the next box to the result

    • Write down the input value after all opposite operations have been completed

• You will need to be able to draw input/output diagrams

• Function questions may involve different mathematical topic areas such as sequences or coordinates or simple algebra