$f(x)=\frac{2x}{2x+3}f(x)\backslash ;=\backslash ;\backslash frac\{2x\}\{2x+3\}$

Setze $x=10x\; =\; 10$, $x=100x=100$ und $x=1000x=1000$ ein.

$f(10)=\frac{2\cdot 10}{2\cdot 10+3}\approx \mathrm{0,869}f(10)\backslash ;=\backslash ;\backslash frac\{2\backslash cdot10\}\{2\backslash cdot10+3\}\backslash approx\backslash ;0\{,\}869$

$f(100)=\frac{2\cdot 100}{2\cdot 100+3}\approx \mathrm{0,985}f(100)\backslash ;=\backslash ;\backslash frac\{2\backslash cdot100\}\{2\backslash cdot100+3\}\backslash approx\backslash ;0\{,\}985$

$f(1000)=\frac{2\cdot 1000}{2\cdot 1000+3}\approx \mathrm{0,999}f(1000)\backslash ;=\backslash ;\backslash frac\{2\backslash cdot1000\}\{2\backslash cdot1000+3\}\backslash approx\backslash ;0\{,\}999$

$f(x)=\frac{2x}{2x+3}f(x)=\backslash frac\{2x\}\{2x+3\}$

$D_f=R\mathrm{\backslash }\{-\mathrm{1,5}\}D\_f=R\backslash backslash\backslash left\backslash \{-1\{,\}5\backslash right\backslash \}$

Nullstelle: $x=0\backslash ;x=0$

$f(x)=\frac{2x}{2x+3}f(x)=\backslash frac\{2x\}\{2x+3\}$

Waagrechte Asymptote

Zählergrad = Nennergrad $\Rightarrow \backslash Rightarrow$ Betrachtung der Koeffizenten

$y=1y=1$

Senkrechte Asymptote

bei der Definitionslücke

$x=-\mathrm{1,5}x=-1\{,\}5$