funkcie.mp

numeric d;
numeric ratiox, ratioy;

def mycircle(expr x, y)=
draw (x-d,y)..(x,y+d)..(x+d,y)..(x,y-d)..cycle
enddef;

def myline(expr x, y, z, w) =
save ratioy, ratiox;
ratiox:=(z-x)/(sqrt((z-x)*(z-x)+(w-y)*(w-y)));
ratioy:=(w-y)/(sqrt((z-x)*(z-x)+(w-y)*(w-y)));
draw (x+d*ratiox,y+d*ratioy)--(z-d*ratiox,w-d*ratioy);
enddef;

def mybline(expr x, y, z, w) =
save ratioy, ratiox;
pickup pencircle scaled 1.5pt;
ratiox:=(z-x)/(sqrt((z-x)*(z-x)+(w-y)*(w-y)));
ratioy:=(w-y)/(sqrt((z-x)*(z-x)+(w-y)*(w-y)));
draw (x+d*ratiox,y+d*ratioy)--(z-d*ratiox,w-d*ratioy);
pickup pencircle scaled .5pt;
enddef;

def myarr(expr x, y, z, w) =
save ratioy, ratiox;
ratiox:=(z-x)/(sqrt((z-x)*(z-x)+(w-y)*(w-y)));
ratioy:=(w-y)/(sqrt((z-x)*(z-x)+(w-y)*(w-y)));
drawarrow (x+2*d*ratiox,y+2*d*ratioy)--(z-2*d*ratiox,w-2*d*ratioy);
enddef;

def xmark(expr s, x) =
draw (x,-dx)--(x,dx);
label.bot (s,(x,-dx));
enddef;

def ymark(expr s, x) =
draw (-dy,x)--(dy,x);
label.lft (s,(-dy,x));
enddef;


verbatimtex \input amstex \loadmsam \loadmsbm \input amssym etex

%vardef f(expr x) = (((x)-3)^2) enddef;
%vardef f(expr x) = (((x)-3)*((x)-3)) enddef;
%vardef f(expr x) = (((x)-3)*((x)-3)/3-1) enddef;
%vardef f(expr x) = ((x)*(x)-0.5) enddef;
%vardef f(expr x) = ((x)/((x)+1)) enddef;
vardef f(expr x) = ((x)/(abs(x)+1)) enddef;

beginfig(1)
%numeric x[],y[];
%pair z[];
%
numeric xmin, xmax, xinc;
numeric l[], r[];

%u:=1.5cm;
%u:=5cm;
u:=0.5cm;
d:=0.05u;

ux:=0.5cm;
uy:=3cm;
dx:=0.2cm;
dy:=0.2cm;

%osi
drawarrow (-11ux,0)--(12ux,0);
drawarrow (0,-1.1uy)--(0,1.2uy);
path osx;
osx:=(-0.5ux,0)--(11ux,0);
label.bot (btex $x$ etex, (11.5ux,0));
label.lft (btex $y$ etex, (0,1.1uy));
label.llft ("0", (0,0));

%xmarks
draw (10ux,-dx)--(10ux,dx);
label.bot ("10",(10ux,-dx));
draw (-10ux,-dx)--(-10ux,dx);
label.bot ("-10",(-10ux,-dx));

%ymarks
%draw (-dy,uy)--(dy,uy);
label.ulft ("1",(-dy,uy));
%draw (-dy,-uy)--(dy,-uy);
label.llft ("-1",(-dy,-uy));

%asymptotes
draw (-11ux,uy)--(11ux,uy);
draw (-11ux,-uy)--(11ux,-uy);

%function plot
%xmin:=0.2;
%xmax:=1;
xmin:=-10.05;
xmax:=10.05;
xinc:=0.05;
path pts_f;
pts_f := (xmin*ux,f(xmin)*uy)
  for x=xmin step xinc until xmax:
    ..((x+xinc)*ux,f(x+xinc)*uy)
%    ..(x*ux,f(x)*uy)
  endfor;
draw pts_f withpen pencircle scaled 1pt;

%labels
label.rt (btex $y=\frac{x}{|x|+1}$ etex, (10ux,0.9uy))

endfig;

vardef f(expr x) = ((x)/(1-abs(x))) enddef;

beginfig(2)

numeric xmin, xmax, xinc;

%u:=1.5cm;
%u:=5cm;
u:=0.5cm;
d:=0.05u;

ux:=3cm;
uy:=0.5cm;
dx:=0.2cm;
dy:=0.2cm;

%osi
drawarrow (-1.1ux,0)--(1.2ux,0);
drawarrow (0,-11uy)--(0,12uy);
label.bot (btex $x$ etex, (1.15ux,0));
label.lft (btex $y$ etex, (0,11uy));
label.llft ("0", (0,0));

%xmarks
label.rt ("1",(ux,-dx));
label.lft ("-1",(-ux,-dx));

%ymarks
ymark("10",10uy);
ymark("-10",-10uy);

%asymptotes
draw (ux,-11uy)--(ux,11uy);
draw (-ux,-11uy)--(-ux,11uy);

%function plot
%xmin:=0.2;
%xmax:=1;
xmin:=-0.9;
xmax:=0.9;
xinc:=0.05;
path pts_f;
pts_f := (xmin*ux,f(xmin)*uy)
  for x=xmin step xinc until xmax:
    ..((x+xinc)*ux,f(x+xinc)*uy)
%    ..(x*ux,f(x)*uy)
  endfor;
draw pts_f withpen pencircle scaled 1pt;

%labels
label.lft (btex $y=\frac{x}{1-|x|}$ etex, (0.9ux,f(0.9)*uy));

endfig;

vardef tand primary x = (sind(x)/cosd(x)) enddef;
vardef f(expr x) = ((tand((x)*90))) enddef;

beginfig(3)

numeric xmin, xmax, xinc;

%u:=1.5cm;
%u:=5cm;
u:=0.5cm;
d:=0.05u;

ux:=1.3cm;
uy:=0.5cm;
dx:=0.2cm;
dy:=0.2cm;

%osi
drawarrow (-1.3ux,0)--(1.5ux,0);
drawarrow (0,-6.5uy)--(0,6.5uy);
label.bot (btex $x$ etex, (1.45ux,0));
label.lft (btex $y$ etex, (0,6.3uy));
label.llft ("0", (0,0));

%xmarks
label.lrt (btex $\frac\pi2$ etex,(ux,0));
label.llft (btex $-\frac\pi2$ etex,(-ux,0));

%ymarks
%ymark("10",10uy);
%ymark("-10",-10uy);

%asymptotes
draw (ux,-6.5uy)--(ux,6.5uy);
draw (-ux,-6.5uy)--(-ux,6.5uy);

%function plot
%xmin:=0.2;
%xmax:=1;
xmin:=-0.9;
xmax:=0.9;
xinc:=0.05;
path pts_f;
pts_f := (xmin*ux,f(xmin)*uy)
  for x=xmin step xinc until xmax:
    ..((x+xinc)*ux,f(x+xinc)*uy)
%    ..(x*ux,f(x)*uy)
  endfor;
draw pts_f withpen pencircle scaled 1pt;

%labels
label.rt (btex $y=\operatorname{tg}(x)$ etex, (ux,f(0.9)*uy));

endfig;

beginfig(4)

%funkcia
vardef f(expr x) = (12-(x)*(x)) enddef;

numeric xmin, xmax, xinc;

%u:=1.5cm;
%u:=5cm;
u:=0.5cm;
d:=0.05u;

ux:=1.3cm;
uy:=0.5cm;
dx:=0.2cm;
dy:=0.2cm;

%osi
drawarrow (-4ux,0)--(4ux,0);
drawarrow (0,-0.5uy)--(0,13.5uy);
label.bot (btex $x$ etex, (4ux,0));
label.lft (btex $y$ etex, (0,13uy));
label.llft ("0", (0,0));

%xmarks
label.lrt (btex $-\sqrt{12}$ etex,(-sqrt(12)*ux,0));
label.llft (btex $\sqrt{12}$ etex,(sqrt(12)*ux,0));

%ymarks
ymark("12",12uy);
%ymark("-10",-10uy);



%function plot
%xmin:=0.2;
%xmax:=1;
xmin:=-3.7;
xmax:=3.7;
xinc:=0.05;
path pts_f;
pts_f := (xmin*ux,f(xmin)*uy)
  for x=xmin step xinc until xmax:
    ..((x+xinc)*ux,f(x+xinc)*uy)
%    ..(x*ux,f(x)*uy)
  endfor;
draw pts_f withpen pencircle scaled 1pt;

%rectangle
a:=2;
draw (a*ux,0)--(a*ux,f(a)*uy)--(-a*ux,f(a)*uy)--(-a*ux,0);

%labels
label.rt (btex $y=12-x^2$ etex, (3.7ux,f(3.7)*uy));
label.bot (btex $x$ etex, (a*ux,0));
label.bot (btex $-x$ etex, (-a*ux,0));
label.urt (btex $12-x^2$ etex, (0,f(a)*uy));

endfig;


beginfig(5)

%funkcia
vardef f(expr x) = (2+sind(360*(x))) enddef;

numeric xmin, xmax, xinc;

%u:=1.5cm;
%u:=5cm;
u:=0.5cm;
d:=0.05u;

ux:=3cm;
uy:=0.5cm;
dx:=0.2cm;
dy:=0.2cm;



%osi
drawarrow (-.5ux,0)--(2.5ux,0);
drawarrow (0,-0.5uy)--(0,3.5uy);

a:=1.3;



%xmarks
label.bot (btex $T$ etex, (ux,-dx));
label.bot (btex $NT$ etex, (2*ux,-dx));
label.bot (btex $a$ etex, (a*ux,-dx));
label.bot (btex $a+T$ etex, ((a+1)*ux,-dx));
label.bot (btex $a-(N-1)T$ etex, ((a-1)*ux,-dx));
draw (ux,-dx)--(ux,dx);
draw (2ux,-dx)--(2ux,dx);
draw (a*ux,-dx)--(a*ux,dx);
draw ((a+1)*ux,-dx)--((a+1)*ux,dx);
draw ((a-1)*ux,-dx)--((a-1)*ux,dx);

%function plot
%xmin:=0.2;
%xmax:=1;
xmin:=-0.3;
xmax:=2.3;
xinc:=0.05;
path pts_f;
pts_f := (xmin*ux,f(xmin)*uy)
  for x=xmin step xinc until xmax:
    ..((x+xinc)*ux,f(x+xinc)*uy)
%    ..(x*ux,f(x)*uy)
  endfor;
draw pts_f withpen pencircle scaled 1pt;

%lines
draw (ux,0)--(ux,f(1)*uy);
draw (2*ux,0)--(2*ux,f(2)*uy);
draw (a*ux,0)--(a*ux,f(a)*uy);
draw ((a+1)*ux,0)--((a+1)*ux,f(a+1)*uy);
draw ((a-1)*ux,0)--((a-1)*ux,f(a-1)*uy);

%fill
xmin:=a; xmax:=2;
pts_f := (xmin*ux,0)--(xmin*ux,f(xmin)*uy)
  for x=xmin step xinc until xmax:
    ..((x+xinc)*ux,f(x+xinc)*uy)
%    ..(x*ux,f(x)*uy)
  endfor
  --(xmax*ux,f(xmax)*uy)--(xmax*ux,0)--cycle;
fill pts_f withcolor .9white;

%fill
xmin:=a-1; xmax:=1;
pts_f := (xmin*ux,0)--(xmin*ux,f(xmin)*uy)
  for x=xmin step xinc until xmax:
    ..((x+xinc)*ux,f(x+xinc)*uy)
%    ..(x*ux,f(x)*uy)
  endfor
  --(xmax*ux,f(xmax)*uy)--(xmax*ux,0)--cycle;
fill pts_f withcolor .9white;

%fill
xmin:=2; xmax:=a+1;
pts_f := (xmin*ux,0)--(xmin*ux,f(xmin)*uy)
  for x=xmin step xinc until xmax:
    ..((x+xinc)*ux,f(x+xinc)*uy)
%    ..(x*ux,f(x)*uy)
  endfor
  --(xmax*ux,f(xmax)*uy)--(xmax*ux,0)--cycle;
fill pts_f withcolor .3white;

%fill
xmin:=0; xmax:=a-1;
pts_f := (xmin*ux,0)--(xmin*ux,f(xmin)*uy)
  for x=xmin step xinc until xmax:
    ..((x+xinc)*ux,f(x+xinc)*uy)
%    ..(x*ux,f(x)*uy)
  endfor
  --(xmax*ux,f(xmax)*uy)--(xmax*ux,0)--cycle;
fill pts_f withcolor .3white;


endfig;



beginfig(6)


numeric xmin, xmax, xinc;

%u:=1.5cm;
%u:=5cm;
u:=0.5cm;
d:=0.05u;

ux:=10cm;
uy:=3cm;
dx:=0.2cm;
dy:=0.2cm;

%osi
drawarrow (-.1ux,0)--(1.2ux,0);
drawarrow (0,-0.5uy)--(0,1.2uy);

s:=.5ux;
a:=.4ux;
b:=.3ux;

%xmarks
label.bot (btex $\frac12$ etex, (s,-dx));
label.bot (btex $\frac12-\frac1m$ etex, (b,-dx));
label.bot (btex $\frac12-\frac1n$ etex, (a,-dx));
draw (a,-dx)--(a,dx);
draw (b,-dx)--(b,dx);
draw (s,-dx)--(s,dx);

%ymarks
ymark("1",1uy);

%lines

draw (s,0)--(s,uy);

%function plot
pickup pencircle scaled 1pt;
draw (0,0)--(a,0)--(s,uy)--(ux,uy);
draw (0,0)--(b,0)--(s,uy)--(ux,uy);

endfig;

\end