# How to make a cobweb diagram

I am struggling making a cobweb diagram for the function $$x_{t+1}=8x_t/{1+2x_t}$$

So I understand when making the cobweb diagram, that I have to draw the line $y=x$

But where I have trouble understanding is how to draw the function in the graph. I am given the point $x_0 =0.5$ So I plug this into the function and get $2 = x_1$ and then I keep plugging in points. Do I graph points like $.5,2$ or $0,.5$?

• I hope this doesn't come across as advertising. In the UK a lot of schools use a piece of software called Autograph. It draws cobweb diagrams for you... and shows Newton-Raphson working, too. – tomi Mar 13 '15 at 9:24

Let the expression on the right be $g(x)$. The method converges (sometimes) to the solution of the equation $x=g(x)$.

The cobweb diagram illustrates the movement from first guess $x_0$ to second guess $x_1$ etc.

Draw a line from $(x_0,0)$ up to $(x_0,x1)$.

Then across to $(x_1,x_1)$.

Then up or down to $(x_1,x_2)$.

Then across to $(x_2,x_2)$.

Etc