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.
- How are the endpoints of the image interval \(f_4(I)\) determined?
- For a point in the image interval, how many points in the domain interval \(I\) get mapped onto that point?
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 \(f_4(I)\).
- How are endpoints of the image interval \(f_4(I)\) determined?
- For a point in the image interval, how many points in the domain interval \(I\) get mapped onto that point?
xmin \(<\) xmax and the applet will still work,
but the labels may be confusing.
xmax:
xmin: