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Graphs act as mathematical models for real-life situations.

Graphs are in their most basic forms rough sketches of a phenomenon--they do not show perfectly the real world phenomenon, but act as an idealization.

Mathematicians must be careful to find a graph which allows them to find trends. Trends are predictions--example, the population will be 40,000 in city XYZ in year 2025. At the same time, mathematicians need to stay with the imperfection of real-world occurrences.

In sum, graphs display real world events--throwing a football, the number of deaths in 1908 versus in 2008, how fast a colony of bacteria grow--but display them in an idealized form.

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