Chapter 8, Explorations 6-7

Use the sliders below to choose the left and right endpoints xmin and xmax of an input interval \(I\) so that both endpoints have values less than \(\frac{1}{2}\). The interval \(I\) you have chosen is in blue and it's image under the map \(x_{n+1} = f_4(x_n)\) is in red.

Answer these questions again when xmin and xmax are both greater than \(\frac{1}{2}\). Now take xmin \(< \frac{1}{2} < \) xmax and again use the tool on the website to observe \(f_4(I)\). Note: You may choose xmin \(<\) xmax and the applet will still work, but the labels may be confusing.