// created with Asymptote: The Vector Graphics Language
// using online-editor: http://asymptote.ualberta.ca/

import graph;

real x_max = 12.5;    // maximum of x-range

unitsize(1cm,10cm);   // aspect ratio x:y=1:10

draw((0,0.5)--(x_max,0.5), heavygreen+dashdotted);   // draw symmetry-axis y=0.5
draw((0,0)--(0,1));                                  // draw y-axis
draw((0,0)--(x_max,0), heavygreen+dashed);           // draw x-axis
draw((0,1)--(x_max,1), heavygreen+dashed);           // draw (y=1)-axis

real f1(real x) {return x/(x+1);}   // definition of function 1
real f2(real x) {return 1/(x+1);}   // definition of function 2

draw(graph(f1,0,x_max), red+2*linewidth(), "$f_1(x) = \frac{x}{x+1}$");               // draw graph of function 1
draw(graph(f2,0,x_max), blue+longdashed+2*linewidth(), "$f_2(x) = \frac{1}{x+1}$");   // draw graph of function 2

xaxis("$x$", BottomTop, LeftTicks(pTick=lightgrey, ptick=palegrey, extend=true));                  // draw x-axis
yaxis("$P$", LeftRight, RightTicks(trailingzero, pTick=lightgrey, ptick=palegrey, extend=true));   // draw y-axis

attach(legend(), point(E), 16W, UnFill);   // draw legend

label("$\lim \limits_{x \to \infty} \frac{x}{x+1} = 1$", (8,0.95), heavygreen, Fill(0.5mm, white));   // add label for limit of function 1; [UnFill(0.5mm) seems not to work in all environments]
label("$\lim \limits_{x \to \infty} \frac{1}{x+1} = 0$", (8,0.05), heavygreen, Fill(0.5mm, white));   // add label for limit of function 2; [UnFill(0.5mm) seems not to work in all environments]