coth x if x > 0
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).