How do you graph $f(x)=x/(x+2)$ ?

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Answer 1 · 2015-07-01T22:53:18

$f(x) = x/(x+2) = 1-2/(x+2)$

As $x -> -oo$ then $f(x) -> 1_+$

As $x -> -2_-$ then $f(x) -> oo$

As $x -> -2_+$ then $f(x) -> -oo$

$f(0) = 0$

As $x -> oo$ then $f(x) -> 1_-$

$f(x) = x/(x+2) = (x+2-2)/(x+2) = (x+2)/(x+2)-2/(x+2)$

$= 1-2/(x+2)$

with exclusion $x != -2$

So it is clear that for large $x$ , $f(x)$ is asymptotic to $1$ and that $f(x)$ has a simple pole at $x = -2$

graph{x/(x+2) [-10, 10, -5, 5]}

How do you graph f(x)=x/(x+2)f(x)=x/(x+2)?