SOLUTION: Find the domain and range of the function f={(x,x^2/1+x^2):x belongs to R}.

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Question 890728: Find the domain and range of the function f={(x,x^2/1+x^2):x belongs to R}.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Domain : All x, no restrictions.
Since both numerator and denominator are squared, there are no negative values.
The minimum value occurs when x=0 and equals 0.
As x approaches infinity,
lim%28x-%3Einfinity%2Cf=1%2F%281%2Fx%5E2%2B1%29=1%2F%289%2B1%29=1%29
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.
.
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E2%2F%281%2Bx%5E2%29%29
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.
.
So the range is [0,1).