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Graph transformations
A-level
Translations, stretches and reflections — and the one rule that sorts them out: inside the bracket is horizontal and does the opposite of what you expect. Flip on Test yourself to drill them.
Inside the bracket = horizontal & opposite; outside = vertical & as expected.
Translations
| f(x) + a | translate UP by aoutside the bracket → vertical, and it does what you'd expect |
| f(x) − a | translate DOWN by a |
| f(x + a) | translate LEFT by ainside the bracket → horizontal, and the OPPOSITE way |
| f(x − a) | translate RIGHT by a |
Stretches
| a·f(x) | vertical stretch, scale factor a |
| f(ax) | horizontal stretch, scale factor 1/ainside the bracket → horizontal, and the reciprocal |
Reflections
| −f(x) | reflection in the x-axis |
| f(−x) | reflection in the y-axis |
The rest of the formulae
Exact trig values, calculus results and identities worth knowing cold.
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