Algebra · Graphs of functions
Chapter 1 · 4
The idea
Cubic, reciprocal and exponential graphs
The shape vocabulary of the Higher course — S-curve cubics, two-branch reciprocals with asymptotes, ever-positive exponentials — and why each equation forces its shape.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Algebra · Graphs of functions
Cubic, reciprocal and exponential graphs
The shape vocabulary of the Higher course — S-curve cubics, two-branch reciprocals with asymptotes, ever-positive exponentials — and why each equation forces its shape.
Why it works
Shape follows formula
Exams show a curve and ask "which equation?" — or name an equation and expect its shape on sight. Each family's shape follows from how its formula treats .The cubic: an S, never a U
Cubing keeps the sign — negative in, negative out — so the curve comes from far BELOW on the left, flattens through , and climbs away to the right. No mirror symmetry (that's the giveaway against a parabola: a parabola U-turns; a cubic never does). With a negative coefficient, , the S runs the other way. A factorised cubic like crosses the -axis at every root: .Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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