Defining Arccosecant The range of the cosecant function is

Chapter 4, Problem 4.1.1.633

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Defining Arccosecant The range of the cosecant function is \((-\infty,\ -1]\cup[1,\ \infty)\), which must become the domain of the arccosecant function. The graph of y = arccsc x must therefore be the union of two unbroken curves. Two possible graphs with the correct domain are shown below.

(a) The graph on the left has one horizontal asymptote. What is it?

(b) The graph on the right has two horizontal asymptotes. What are they?

(c) Which of these graphs is also the graph of \(y=\sin ^{-1}(1 / x)\)?

(d) Which of these graphs is decreasing on both connected intervals?

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