SOLUTION: Consider the rational function f (x) =2x/x-1 . Give: (i) The domain. (ii) The Vertical Asymptote. (iii) The Horizontal Asymptote. (iv) The graph. Please help me to solve

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Question 34601: Consider the rational function f (x) =2x/x-1 . Give:
(i) The domain.
(ii) The Vertical Asymptote.
(iii) The Horizontal Asymptote.
(iv) The graph.
Please help me to solve this problem. I am no good with rational functions. Thank you.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
y=2x/(x-1)
a) Domain?
The denominator cannot be zero, so x cannot be 1.
Domain: all real numbers except x=1
b)Vertical Asymptote
As x gets closer and closer to x=1 the fraction get larger and larger;
that means y gets larger and larger; that means you have a vertical
asymptote at x=1
c)Horizontal Asymptote
As x gets very large the 2x/x pretty well determine the value of y.
That means you have a horizontal asymptote at y=2
Cheers,
Stan H.