The idea

Cubic and reciprocal graphs (tables, plotting and asymptotes)

Draw y = x³ − 3x and y = 4/x from a table of values (a cube keeps its sign, and there is no point at x = 0), join the points with one smooth curve (two separate branches for a reciprocal), read the solutions of an equation off the curve, and know the shapes of ±x³ and ±k/x and the asymptotes they never touch.

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 and reciprocal graphs (tables, plotting and asymptotes)

Why it works

An equation no method can solve

Try to solve

x^3 - 3x = 1

. Factorising fails, and no formula in the course fits a cube. Yet the equation has answers, and a graph will find them: draw

y = x^3 - 3x

, and every point where the curve is at height

1

gives a solution. So this page is one job done well. Draw a curve you cannot draw with a ruler, then read it.

The drawing starts with a table. Substitute each

x

, with negatives in brackets:

$x$	$-2$	$-1$	$0$	$1$	$2$
$y$	$-2$	$2$	$0$	$-2$	$2$

Keep reading — free

The rest of the explanation, plus 4 worked examples you step through move by move.

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