Your descriptors are mostly correct, assuming the column headings are something like ...
... function ... domain ... range ... odd/even ... intercepts ... increasing/decreasing ... ??? ... critical points
_____
√x is increasing on the interval [0, ∞). There is no branch where the function is decreasing.
1/x has a critical point at x=0. The slope is undefined there.
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Although the documents mentioned in the question are not included, we can still explain the causes of the rise of nationalism during this period using other sources.
The idea of a "nation" is a modern creation. This idea is widely different to how people thought of themselves in premodern times. Prior to the development of nationalism, people thought of themselves as subjects or followers of a leader. They also identified themselves with their family or village, rather than a large community.
Nationalism only became possible after people began feeling a connection to those who shared their own language, culture and traditions, even when they had never met them before. Two important causes of this were the ideas of liberalism and the Romantic movement.
An important catalyst for this was the rise of liberalism. Liberal ideology encouraged the idea of representation of people in government. Therefore, people began to identify themselves with the government, and to think of themselves as a common people within a political unity. The permanence of people meant that the state did not equal the ruling dynasty. Instead, the king might change, but the nation prevailed.
Nationalism was also born out of Romanticism, which encouraged a romantic view of culture, traditions and common history. It also created a romantic view of land and nationhood. Because of this, there was an attempt to redraw borders to permanently match cultural and linguistic boundaries. Moreover, nationalism encouraged the idea of self-determination.
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