SOLUTION: What are the methods in finding the range and domain of an equation?

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Question 124975: What are the methods in finding the range and domain of an equation?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
What are the methods in finding the range and domain of an equation?
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Here's an example:
y = [sqrt(x-2)]/(x-5)
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Domain:
The denominator must not be zero, so x cannot be 5.
The radicand cannot be negative, so x cannot be less than 2
So the domain is (2,5)U(5,+inf)
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Range:
The easiest way to see the range is to graph the function:
graph%28400%2C300%2C-10%2C30%2C-10%2C30%2C%28x-2%29%5E%281%2F2%29%2F%28x-5%29%29
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The range is all Real Numbers
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If you had [sqrt(x-2)/(x-5)]^2 the domain would not
change but the range would be all Real Numbers greater
that or equal to zero.
graph%28400%2C300%2C-10%2C30%2C-10%2C10%2C%28%28x-2%29%5E%281%2F2%29%2F%28x-5%29%29%5E2%29
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Cheers,
Stan H.