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Section 9.3 · Algebra

Functions and function machines

Use function machines and mapping diagrams, find inputs from outputs, and write a function algebraically.

6 teaching slides 69 practice questions Worked answers for every question

1 · Teaching slidesuse ← → keys

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2 · Key words

functionA rule that turns each input into exactly one output.
function machineA diagram of a function as a chain of operations.
inputThe number that goes in.
outputThe number that comes out.
inverseThe operation that undoes another.
mapping diagramA picture showing which input goes to which output.

3 · Summary of the sectionrevise from this

  • A function turns each input into exactly one output.
  • A function machine shows the operations in order, left to right.
  • To go forwards, apply the operations in order.
  • To go backwards, use the inverse of each operation, in reverse order.
  • Inverses: + and −; × and ÷.
  • Order matters. “× 2 then + 1” is y = 2x + 1; “+ 1 then × 2” is y = 2(x + 1).
  • A mapping diagram draws an arrow from each input to its output.
  • Writing the machine as y = … turns it into algebra, which is where Unit 11 picks it up.
PDFPrintable worksheet All 69 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons1 videos

Function Machines

British corbettmaths

Forwards and backwards through one- and two-step machines, building up to algebraic ones.

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4 · Practice69 questions, easiest first

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