SOLUTION: Given {{{ g(x) = (3x^2+4x-3)/(x^2+3) }}} , determine the horizontal asymptote and the point where the graph crosses the horizontal asymptote

Algebra ->  Functions -> SOLUTION: Given {{{ g(x) = (3x^2+4x-3)/(x^2+3) }}} , determine the horizontal asymptote and the point where the graph crosses the horizontal asymptote      Log On


   

Question 1052526: Given +g%28x%29+=+%283x%5E2%2B4x-3%29%2F%28x%5E2%2B3%29+ , determine the horizontal asymptote and the point where the graph crosses the horizontal asymptote
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%5E2%2B4x-3%29%2F%28x%5E2%2B3%29=%283%2B4%2Fx-3%2Fx%5E2%29%2F%281%2B3%2Fx%5E2%29
In the limit as x goes to infinity and -infinity,
g%28x%29=3
So the horizontal asymptote is y=3.
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Crossing the horizontal asymptote,
%283x%5E2%2B4x-3%29%2F%28x%5E2%2B3%29=3
3x%5E2%2B4x-3=3x%5E2%2B9
4x=12
x=3
Then,
y=%283%283%29%5E2%2B4%283%29-3%29%2F%283%5E2%2B3%29=%2827%2B12-3%29%2F%289%2B3%29=36%2F12=3
(3,3)
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