Question

What is the largest open interval over which f left parenthesis x right parenthesis equals StartFraction 1 Over x EndFraction
​increases, decreases, and is​ constant?
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Part 1
What is the largest open interval over which f left parenthesis x right parenthesis equals StartFraction 1 Over x EndFraction
​increases? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The open interval is
  
enter your response here.
​(Type your answer in interval notation. Use a comma to separate answers as​ needed.)
B.
None
Part 2
What is the largest open interval over which f left parenthesis x right parenthesis equals StartFraction 1 Over x EndFraction
​decreases? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The open​ interval(s) is/are
  
enter your response here.
​(Type your answer in interval notation. Use a comma to separate answers as​ needed.)
B.
None
Part 3
What is the largest open interval over which f left parenthesis x right parenthesis equals StartFraction 1 Over x EndFraction
is​ constant? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The open interval is
  
enter your response here.
​(Type your answer in interval notation. Use a comma to separate answers as​ needed.)
B.
None
What is the largest open interval over which f left parenthesis x right parenthesis equals StartFraction 1 Over x EndFraction increases, decreases, and is constant?Select the correct choice below and, if necessary, fill in the answer box to complete your choice.input field 2Select the correct choice below and, if necessary, fill in the answer box to complete your choice.input field 3Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Answer 1

f(x) = 1/x, domain (-∞,0) ∪ (0,∞). f'(x) = -1/x^2 < 0 for every x ≠ 0.

- Increases: None.
- Decreases: (-∞,0) and (0,∞).
- Constant: None.