What is the Range of a Rational Function?

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The discussion focuses on finding the range of the rational function y = 1/(x + 1). Participants clarify the importance of understanding both domain and range, emphasizing that the domain excludes x = -1. For x < -1, the range of y values is negative (y < 0), while for x > -1, the range is positive (y > 0). Consequently, the overall range of the function is all real numbers except zero (y ≠ 0). The conversation highlights methods for determining the range, including inverting the function and analyzing asymptotic behavior.
  • #31
Thanks for the help, and just to be sure, the range is always expressed as y \neq ...
 
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  • #32
No, only sometimes, like here.
 

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