coth x if x > 0
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on the domain D = (−∞, ∞), where coth x = cosh(x)/ sinh(x).

(a) Give the range of R of f(x). Justify your answer.
(b) By considering each sub-interval separately, construct a hand drawn sketch of y = f(x) in the portion of the xy-plane given by x ∈ (−5, 5) and y ∈ (−5, 5).
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