Q:

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 $0,.5$? 

A:

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

