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

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The discussion focuses on determining the domain of variables in rational functions. For the function y - 1, the domain is all real numbers (R). In the case of (2y)/(y - 1), the variable y cannot equal 1, leading to the domain expressed as D = {y | y ≠ 1}. The interval notation for this domain is (-∞, 1) U (1, ∞). Understanding these domains is essential for working with rational functions effectively.
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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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