lesson
A reciprocal graph has a restriction
1 · Learn
For y = k/x with non-zero k, x cannot equal zero. As positive x grows, positive y decreases when k is positive. The graph approaches the axes but does not cross them in this model.
A reciprocal relationship is not a straight decreasing line. Equal increases in x do not cause equal decreases in y.
2 · Worked example
For y = 12/x, x = 1,2,3,6 gives y = 12,6,4,2. The product stays 12.
3 · Your turn
For y = 18/x, find y at x = 3 and x = 9.
Check your answer
6 and 2.
4 · Apply your learning
Plot values on both sides of zero and explain why zero must be excluded.
Adult guidance and safety
Check prerequisites, units and reasoning. Provide accurate diagrams and varied practice. Extension content needs suitable prior understanding; no GCSE board, tier or examination readiness is implied by this proposed sequence.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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