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Calculus/Functions and their graphs

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Expert: - 2/6/2010


Question
Define f(x) to be the larger of x and 2-x. Sketch the graph f(x). What are its domain and range? Express f(x) in therms of absolute value functions?

Answer
The graph will be in the form of a V with 45° slopes that has a vertex at (2,0).
The domain is all x and the range is all ył>=0.

To define it in terms of an absolute value, f(x) = |2-x|.
It could also be said f(x) =|x-2|, since |x-2| = |2-x|.

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