Question: Consider a function f which is continuous on (,1) and (1,), has a vertical asymptote x = 1, has a horizontal asymptote y = 0,

Consider a function f which is continuous on (,1) and (1,), has a vertical asymptote x = 1, has a horizontal asymptote y = 0, and for which the following conditions hold: f(2) = 1,f(1) = 2,f(0) = 0,f(2) = 2 f(x) > 0 on (1,1) f(x) < 0 on (,1),(1,) f(x) = 0 at x = 1 f(x) > 0 on (2,1),(1,) f(x) < 0 on (,2) f(x) = 0 at x = 2. Sketch the graph of f(x). Clearly show your reasoning regarding the shape of the graph and show concavity accurately.

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