Here is the plot of the piecewise function $g(x)$, restricted to the domain $[0, 1]$ and range $[0, 1]$. The function is limited to this interval, showing how it behaves within the specified bounds.

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Here are some related questions you might be interested in:

1. How do you determine the range of a piecewise function?
2. What are the implications of restricting the domain and range of a function?
3. How does the graph of $g(x)$ differ when its range is not restricted?
4. Can you explain how to find the points of intersection for this function within the given domain?
5. What is the significance of the slope within the restricted range?
6. How do you solve inequalities involving piecewise functions?
7. What are the challenges in graphing piecewise functions with restricted domains?
8. How would you extend this function beyond the interval $[0, 1]$?

Tip: When working with restricted domains and ranges, always double-check that the function values adhere to the specified intervals, particularly if the function involves discontinuities or sharp changes.