The iterative formula
Type the formula with $x$ for $x_n$ (sqrt for √, / for a fraction, ^ for a power; ∛ is under ⌨ Maths keys, ⋯ More keys), e.g. $\sqrt{3 - x}$. Drag the orange ring on the $x$-axis to move $x_0$.
How the diagram works
We want $x = \mathrm{g}(x)$: that is where the line $y = x$ meets the curve $y = \mathrm{g}(x)$.
From $x_n$ go up (or down) to the curve: the height there is $\mathrm{g}(x_n) = x_{n+1}$. Then go across to $y = x$: on that line $y$ and $x$ are equal, so the height becomes the $x$-value $x_{n+1}$, dropped to the $x$-axis. That is why $y = x$ is drawn. Repeat from $x_{n+1}$.
Change of sign
Examples
Your answer
Print a sheet
Graphs of $y = x$ and $y = \mathrm{g}(x)$ for students to draw the staircase or cobweb diagrams on, then the answers: draw the first three steps, draw the next steps from the first, or find $x_1$, $x_2$ and $x_3$ (GCSE or A Level functions, as chosen at the top).
Create your own question
My questions
Kept on this device. To set them for the class, open 👥 Class activity: each of your questions is a level there (Own 1, Own 2, …), or press “My own questions, in order”.