SOLUTION: Decide whether each relation defines Y as a function of X. Give the domain and range. xy=3 Does the relation define a function?

SOLUTION: Decide whether each relation defines Y as a function of X. Give the domain and range. xy=3 Does the relation define a function? - I answered Yes What is the domain and wh

Question 707830: Decide whether each relation defines Y as a function of X. Give the domain and range.
xy=3
Does the relation define a function? - I answered Yes
What is the domain and what is the range?
The answer is Domain = (- infinity, 0) union (0, infinity)
Range = (- infinity, 0) union (0, infinity)
HOW DO I GET THIS ANSWER? WHAT ARE THE SPECIFIC STEPS?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
xy = 3

y = 3/x

So this is a function. This is a function because you can plug in any x number and get EXACTLY ONE y value as an output.

The variable x can be any number but it can't equal 0 because you can't divide by zero.

So that's why the domain is (- infinity, 0) union (0, infinity)

Similarly, if you solve for x, you get

x = 3/y

and the range will be any y value but y can't equal zero either.

So the range is the same as the domain, which means the range is: (- infinity, 0) union (0, infinity)
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