You have already met the gentle U of the quadratic graph. Two more equations have shapes worth knowing on sight: the cubic y = x^3 and the reciprocal y = \dfrac{1}{x}. Learning a graph by its shape lets you sketch a function without plotting dozens of points.

The cubic: y = x³

Cubing keeps the sign of the input: a negative number cubed stays negative, a positive number cubed stays positive, and 0^3 = 0. So the curve sweeps up from the bottom-left, flattens as it passes through the origin, then climbs steeply to the top-right — a smooth S-shape.

Notice it grows far faster than the quadratic: by x = 3 the cubic has already reached 27.

The reciprocal: y = 1/x

Dividing 1 by a number reverses its size: large inputs give tiny outputs, and tiny inputs give huge outputs. There is no value at x = 0 — you cannot divide by zero — so the graph splits into two separate branches: one in the top-right (both coordinates positive) and one in the bottom-left (both negative).

Each branch creeps toward the axes but never touches them: as x grows the curve hugs the x-axis, and near x = 0 it shoots up (or down) alongside the y-axis. Lines a curve approaches but never reaches are called asymptotes — here the two axes are the asymptotes.