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Functions and how to represent them sheet
5-mark answer frame

Represent a given function as an arrow diagram, a table and a graph.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Write what is given and what is to be found. Copy f. Note the domain (first entries) and the images (second entries).
  2. 2 · Write the formula or theorem. f is a function when every element of the domain has exactly one image.
  3. 3 · Draw the arrow diagram. Two labelled ovals, A and B, with one arrow from each x to f(x).
  4. 4 · Make the table. Two rows: x in the top row and f(x) under each x.
  5. 5 · Draw the graph.
    • Draw and label both axes; write the scale.
    • Plot each pair (x, f(x)) as a dot.
    • Do not join the dots when the domain is a finite set.
  6. 6 · Check and box the answer. Count the arrows, table columns and dots: each count must equal the number of pairs.

Scoring tip: Use a sharp pencil and write the scale, for example 'x-axis: 1 cm = 1 unit, y-axis: 1 cm = 1 unit', in the top corner of the graph.