# 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?

**Note:**You may choose

`xmin`

\(<\) `xmax`

and the applet will still work,
but the labels may be confusing.
xmax:

xmin: