A-level maths / Pure 1 / Graphs and transformations
Graphs and transformations
Read a curve, explain its shape and understand what changes when its equation changes.
Choose a lesson or a section directly. Keep the working in view while you control the graph and explore an optional animation.
- Cubic and quartic graphsSketch cubic and quartic graphs using roots, repeated factors, intercepts and end behaviour. Recover equations from graph features and practise with full solutions.
- Reciprocal graphsUnderstand y = k/x and y = k/x², sketch their branches and asymptotes, compare scales and find translated reciprocal graphs.
- Solving equations with graphsUse graph intersections to solve equations, count real solutions, recognise tangencies and rearrange an equation to use a known graph.
- Graph transformationsLearn translations, stretches and reflections of y = f(x). Map points, roots and asymptotes, combine transformations and find unknown parameters.
Useful foundations
Review factorising to find roots or quadratic graphs for intercepts, turning points, domain and range.