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 January 7th, 2011, 04:34 AM #1 Senior Member   Joined: Dec 2010 Posts: 233 Thanks: 0 Functions Sketch the graph,label the asymptotes and state the range 1. f(x) = x+1 / x-3 ,x ?R,x?3 2. y= x+1 / (x-1)(x-2) please help me to solve the question. i only know to find x=3,x=-1/3
January 7th, 2011, 05:37 AM   #2
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Re: Functions

1. f(x) = (x +1)/(x - 3), x ? R, x ? 3

There's a vertical asymptote at x = 3. Do you see why?

$\lim_{x \to \infty^{\pm}}\frac{x\,+\,1}{x\,-\,3}\,=\,1\,\Rightarrow\,\tex{Horizontal asymtote at }y\,=\,1$

Zeros at x = 3, x = -1; test between and outside of this interval:

x > 3, function is positive
-1 < x < 3, function is negative
x < -1, function is positive

Range: (-?, 1) U (1, ?)
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