What is the Domain of Each Variable in a Rational Function?

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SUMMARY

The domain of the variable y in the rational function y - 1 is all real numbers, denoted as R. For the function (2y)/(y - 1), the domain excludes the value y = 1, resulting in D = {y | y ≠ 1}. In interval notation, this domain is expressed as y = (-∞, 1) U (1, ∞). This notation is essential for accurately representing domains and ranges in mathematical contexts.

PREREQUISITES
  • Understanding of rational functions
  • Familiarity with interval notation
  • Basic algebraic manipulation skills
  • Knowledge of real number properties
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  • Study the properties of rational functions
  • Learn how to determine the domain of various functions
  • Practice converting between set notation and interval notation
  • Explore advanced topics in function analysis, such as limits and asymptotes
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Students studying algebra, mathematics educators, and anyone interested in mastering the concepts of rational functions and their domains.

mathdad
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Specify the domain of each variable.

1. y - 1

Well, y can be any integer. So, the domain is R, where R = ALL REAL NUMBERS.

2. (2y)/(y - 1)

y - 1 = 0

y = 1

Let D = domain

D = {y| y CANNOT be 1}

Correct?
 
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Correct. :D

Can you state the domains using interval notation? It's a commonly employed notation that students should be able to utilize when stating domains/ranges, etc.
 
If memory serves me right, the interval notation is

y = (-∞,1) U (1,∞)
 

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