What is the Range of a Rational Function?

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SUMMARY

The range of the rational function y = 1/(x + 1) is all real numbers except for zero (y ≠ 0). This conclusion is derived from analyzing the function's behavior as x approaches -1 and infinity. For x < -1, y can take negative values approaching zero but never reaching it, while for x > -1, y can take positive values also approaching zero but never reaching it. Thus, the complete range is expressed as {y | y ≠ 0} or in interval notation as (-∞, 0) ∪ (0, ∞).

PREREQUISITES
  • Understanding of rational functions
  • Knowledge of domain and range concepts
  • Familiarity with asymptotic behavior of functions
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Study the concept of horizontal and vertical asymptotes in rational functions
  • Learn how to invert rational functions to find their ranges
  • Explore interval notation and its applications in expressing ranges
  • Practice finding the range of other rational functions
USEFUL FOR

Students in algebra or calculus courses, educators teaching rational functions, and anyone seeking to understand the properties of rational functions and their ranges.

  • #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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