How do you graph $f (x) = \frac{x}{x + 2}$ $f(x)=x/(x+2)$ ?

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Answer 1 · 2015-07-01T22:53:18

$f (x) = \frac{x}{x + 2} = 1 - \frac{2}{x + 2}$ $f(x) = x/(x+2) = 1-2/(x+2)$

As $x \to - \infty$ $x -> -oo$ then $f (x) \to 1_{+}$ $f(x) -> 1_+$

As $x \to - 2_{-}$ $x -> -2_-$ then $f (x) \to \infty$ $f(x) -> oo$

As $x \to - 2_{+}$ $x -> -2_+$ then $f (x) \to - \infty$ $f(x) -> -oo$

$f (0) = 0$ $f(0) = 0$

As $x \to \infty$ $x -> oo$ then $f (x) \to 1_{-}$ $f(x) -> 1_-$

$f (x) = \frac{x}{x + 2} = \frac{x + 2 - 2}{x + 2} = \frac{x + 2}{x + 2} - \frac{2}{x + 2}$ $f(x) = x/(x+2) = (x+2-2)/(x+2) = (x+2)/(x+2)-2/(x+2)$

$= 1 - \frac{2}{x + 2}$ $= 1-2/(x+2)$

with exclusion $x \neq - 2$ $x != -2$

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

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

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