input mp-tool;

%prologues:=0;

%pi
numeric pi;
pi:=3.14159;

%cos function for radian input
def cos(expr x)=
 cosd(180/pi*x)
enddef;

%sin function for radian input
def sin(expr x)=
 sind(180/pi*x)
enddef;

%xtick marks
def xtick(expr p)=
 draw ((0,-2pt)--(0,2pt)) shifted p;
enddef;

%ytick marks
def ytick(expr p)=
 draw ((-2pt,0)--(2pt,0)) shifted p;
enddef;

%opendot
vardef open(expr pos)=
 path p;
 p:=fullcircle scaled 3pt;
 p:=p shifted pos;
 fill p withcolor white;
 draw p withcolor red;
enddef;

beginfig(1);

%Define function to be drawn
def f(expr x)=
 x*(x+2)*(x-2)
enddef;

%Declare and initialize viewing window
numeric xmin, xmax, ymin, ymax;
xmin=-5;
xmax=5;
ymin=-5;
ymax=5;

%Declare and initialize scaling variables
numeric ux, uy;
(xmax-xmin)*ux=2in;
(ymax-ymin)*uy=2in;

%Declare and initialize clipping boundary
path q;
q:=(xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle;
q:=q xscaled ux yscaled uy;

%Declare and initialize number of plotted points
numeric N;
N:=200;

%Declare and calculate plotting increment delta x
numeric dx;
dx:=(xmax-xmin)/N;

%Declare and create function path
path p;
p:=(xmin,f(xmin));
for x=xmin step dx until xmax:
 p:=p--(x,f(x));
endfor;
p:=p--(xmax,f(xmax));

%Scale function path
p:=p xscaled ux yscaled uy;

%Clip function path
draw p;
clip currentpicture to q;

%Save and clear the function path
picture pic;
pic:=currentpicture;
clearit;

%Draw and label coordinate axes
drawdblarrow (1.1xmin*ux,0)--(1.1xmax*ux,0);
label.rt(btex $x$ etex,(1.1xmax*ux,0));
drawdblarrow (0,1.1ymin*uy)--(0,1.1ymax*uy);
label.top(btex $y$ etex,(0,1.1ymax*uy));

%Superimpose function plot
draw pic withcolor blue;

%xtick marks
for k=xmin step 1 until xmax:
 xtick((k*ux,0))
endfor;

%label xticks
label.bot(btex $-5$ etex, (xmin*ux,0));
label.bot(btex $5$ etex, (xmax*ux,0));

endfig;

beginfig(2);

%Define function to be drawn
def f(expr x)=
 x*(x+2)*(x-2)
enddef;

%Declare and initialize viewing window
numeric xmin, xmax, ymin, ymax;
xmin=-5;
xmax=5;
ymin=-5;
ymax=5;

%Declare and initialize scaling variables
numeric ux, uy;
(xmax-xmin)*ux=2in;
(ymax-ymin)*uy=2in;

%Declare and initialize clipping boundary
path q;
q:=(xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle;
q:=q xscaled ux yscaled uy;

%Declare and initialize number of plotted points
numeric N;
N:=200;

%Declare and calculate plotting increment delta x
numeric dx;
dx:=(xmax-xmin)/N;

%Declare and create function path
path p;
p:=(xmin,f(xmin));
for x=xmin step dx until xmax:
 p:=p--(x,f(x));
endfor;
p:=p--(xmax,f(xmax));

%Scale function path
p:=p xscaled ux yscaled uy;

%Clip function path
draw p withcolor blue;

%Highlight parts of the path that are above the axis
p:=(-2,f(-2));
for x = -2 step dx until 0:
 p:=p--(x,f(x));
endfor;
p:=p--(0,f(0));
p:=p xscaled ux yscaled uy;
draw p withcolor red withpen pencircle scaled 1pt;

p:=(2,f(2));
for x = 2 step dx until xmax:
 p:=p--(x,f(x));
endfor;
p:=p--(xmax,f(xmax));
p:=p xscaled ux yscaled uy;
draw p withcolor red withpen pencircle scaled 1pt;

%Draw open circles
open((-2*ux,0));
open((0,0));
open((2*ux,0));

clip currentpicture to q;

%Save and clear the function path
picture pic;
pic:=currentpicture;
clearit;

%Draw and label coordinate axes
drawdblarrow (1.1xmin*ux,0)--(1.1xmax*ux,0);
label.rt(btex $x$ etex,(1.1xmax*ux,0));
drawdblarrow (0,1.1ymin*uy)--(0,1.1ymax*uy);
label.top(btex $y$ etex,(0,1.1ymax*uy));

%Superimpose function plot
draw pic;

%xtick marks
for k=xmin step 1 until xmax:
 xtick((k*ux,0))
endfor;

%label xticks
label.bot(btex $-5$ etex, (xmin*ux,0));
label.bot(btex $5$ etex, (xmax*ux,0));

endfig;

beginfig(3);

%Define function to be drawn
def f(expr x)=
 exp(x)
enddef;

%Declare and initialize viewing window
numeric xmin, xmax, ymin, ymax;
xmin=-5;
xmax=5;
ymin=-5;
ymax=5;

%Declare and initialize scaling variables
numeric ux, uy;
(xmax-xmin)*ux=2in;
(ymax-ymin)*uy=2in;

%Declare and initialize clipping boundary
path q;
q:=(xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle;
q:=q xscaled ux yscaled uy;

%Declare and initialize number of plotted points
numeric N;
N:=200;

%Declare and calculate plotting increment delta x
numeric dx;
dx:=(xmax-xmin)/N;

%Declare and create function path
path p;
p:=(xmin,f(xmin));
for x=xmin step dx until xmax:
 p:=p--(x,f(x));
endfor;
p:=p--(xmax,f(xmax));

%Scale function path
p:=p xscaled ux yscaled uy;

%Clip function path
draw p withcolor blue;

%reflect p about x-axis
draw (p reflectedabout ((0,0),(1,0))) withcolor red;

clip currentpicture to q;

%Save and clear the function path
picture pic;
pic:=currentpicture;
clearit;

%Draw and label coordinate axes
drawdblarrow (1.1xmin*ux,0)--(1.1xmax*ux,0);
label.rt(btex $x$ etex,(1.1xmax*ux,0));
drawdblarrow (0,1.1ymin*uy)--(0,1.1ymax*uy);
label.top(btex $y$ etex,(0,1.1ymax*uy));

%Superimpose function plot
draw pic;

%xtick marks
for k=xmin step 1 until xmax:
 xtick((k*ux,0))
endfor;

%label xticks
label.bot(btex $-5$ etex, (xmin*ux,0));
label.bot(btex $5$ etex, (xmax*ux,0));

%label first curve
label.rt(btex $y=e^x$ etex, (2ux,5uy));

%label second curve
label.rt(btex $y=e^{-x}$ etex, (2ux,-5uy));

endfig;

beginfig(4);

%Define function to be drawn
def f(expr x)=
 exp(x)
enddef;

%Declare and initialize viewing window
numeric xmin, xmax, ymin, ymax;
xmin=-5;
xmax=5;
ymin=-5;
ymax=5;

%Declare and initialize scaling variables
numeric ux, uy;
(xmax-xmin)*ux=2in;
(ymax-ymin)*uy=2in;

%Declare and initialize clipping boundary
path q;
q:=(xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle;
q:=q xscaled ux yscaled uy;

%Declare and initialize number of plotted points
numeric N;
N:=200;

%Declare and calculate plotting increment delta x
numeric dx;
dx:=(xmax-xmin)/N;

%Declare and create function path
path p;
p:=(xmin,f(xmin));
for x=xmin step dx until xmax:
 p:=p--(x,f(x));
endfor;
p:=p--(xmax,f(xmax));

%Scale function path
p:=p xscaled ux yscaled uy;

%Clip function path
draw p reflectedabout ((0,0),(1,0)) shifted (0,1uy) withcolor blue;

clip currentpicture to q;

%Save and clear the function path
picture pic;
pic:=currentpicture;
clearit;

%Draw and label coordinate axes
drawdblarrow (1.1xmin*ux,0)--(1.1xmax*ux,0);
label.rt(btex $x$ etex,(1.1xmax*ux,0));
drawdblarrow (0,1.1ymin*uy)--(0,1.1ymax*uy);
label.top(btex $y$ etex,(0,1.1ymax*uy));

%Superimpose function plot
draw pic;

%xtick marks
for k=xmin step 1 until xmax:
 xtick((k*ux,0))
endfor;

%label xticks
label.bot(btex $-5$ etex, (xmin*ux,0));
label.bot(btex $5$ etex, (xmax*ux,0));

%ytick marks
for k=xmin step 1 until xmax:
 ytick((0,k*uy))
endfor;

%label xticks
label.lft(btex $-5$ etex, (0,ymin*uy));
label.lft(btex $5$ etex, (0,ymax*uy));

%draw in the asymptote
draw (xmin*ux,1uy)--(xmax*ux,1uy) withcolor red dashed evenly;

endfig;

beginfig(5);

%Define function to be drawn
def f(expr x)=
 ln(x-2)
enddef;

%Declare and initialize viewing window
numeric xmin, xmax, ymin, ymax;
xmin=-5;
xmax=5;
ymin=-5;
ymax=5;

%Declare and initialize scaling variables
numeric ux, uy;
(xmax-xmin)*ux=2in;
(ymax-ymin)*uy=2in;

%Declare and initialize clipping boundary
path q;
q:=(xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle;
q:=q xscaled ux yscaled uy;

%Declare and initialize number of plotted points
numeric N;
N:=200;

%Declare and calculate plotting increment delta x
numeric dx;
dx:=(xmax-xmin)/N;

%Declare and create function path
path p;
p:=(2.01,f(2.01));
for x=2.01 step dx until xmax:
 p:=p--(x,f(x));
endfor;
p:=p--(xmax,f(xmax));

%Scale function path
p:=p xscaled ux yscaled uy;

%draw the function
draw p withcolor blue;

%clip
clip currentpicture to q;

%Save and clear the function path
picture pic;
pic:=currentpicture;
clearit;

%Draw and label coordinate axes
drawdblarrow (1.1xmin*ux,0)--(1.1xmax*ux,0);
label.rt(btex $x$ etex,(1.1xmax*ux,0));
drawdblarrow (0,1.1ymin*uy)--(0,1.1ymax*uy);
label.top(btex $y$ etex,(0,1.1ymax*uy));

%Superimpose function plot
draw pic;

%xtick marks
for k=xmin step 1 until xmax:
 xtick((k*ux,0))
endfor;

%label xticks
label.bot(btex $-5$ etex, (xmin*ux,0));
label.bot(btex $5$ etex, (xmax*ux,0));

%draw the asymptote
draw (2ux,ymin*uy)--(2ux,ymax*uy) dashed evenly withcolor red;

%plot key point
drawdot (3ux,0) withpen pencircle scaled 2pt;

%label key point
pic:=thelabel.ulft(btex $(3,0)$ etex, (3ux,0));
unfill bbox pic;
draw pic;

endfig;

beginfig(6);

%initialize scale
numeric u;
10u=2in;

%draw axes
path xaxis,yaxis;
xaxis:=(-5u,0)--(5u,0);
yaxis:=(0,-5u)--(0,5u);
drawdblarrow xaxis scaled 1.1;
drawdblarrow yaxis scaled 1.1;
label.rt(btex $x$ etex, (1.1*u*xmax,0));
label.top(btex $y$ etex, (0,1.1*u*ymax));

%tickmarks
for k=-5u step 1u until 5u:
 xtick((k,0));
 ytick((0,k));
endfor;

%define and plot ellipse
path p;
p:=fullcircle xscaled 2u yscaled 6u;
draw p shifted (1u,-2u) withcolor blue;

%Label the center
drawdot (1u,-2u) withpen pencircle scaled 2pt;

%direction of motion
drawarrow (2u,-2u)--((2u,-2u)+10*down) withpen pencircle scaled 1pt withcolor red;

endfig;

beginfig(7);

%Define function to be drawn
def f(expr x)=
 sqrt(x)
enddef;

%Declare and initialize viewing window
numeric xmin, xmax, ymin, ymax;
xmin=-5;
xmax=5;
ymin=-5;
ymax=5;

%Declare and initialize scaling variables
numeric ux, uy;
(xmax-xmin)*ux=2in;
(ymax-ymin)*uy=2in;

%Declare and initialize clipping boundary
path q;
q:=(xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle;
q:=q xscaled ux yscaled uy;

%Declare and initialize number of plotted points
numeric N;
N:=200;

%Declare and calculate plotting increment delta x
numeric dx;
dx:=(xmax-xmin)/N;

%Declare and create function path
path p;
p:=(0,f(0));
for x=0 step dx until xmax:
 p:=p--(x,f(x));
endfor;
p:=p--(xmax,f(xmax));

%Scale function path
p:=p xscaled ux yscaled uy;

%draw the function
draw p withcolor blue;

%reflect the function across x-axis
draw p reflectedabout ((0,0),(1,0)) withcolor red;

%clip
clip currentpicture to q;

%Save and clear the function path
picture pic;
pic:=currentpicture;
clearit;

%Draw and label coordinate axes
drawdblarrow (1.1xmin*ux,0)--(1.1xmax*ux,0);
label.rt(btex $x$ etex,(1.1xmax*ux,0));
drawdblarrow (0,1.1ymin*uy)--(0,1.1ymax*uy);
label.top(btex $y$ etex,(0,1.1ymax*uy));

%Superimpose function plot
draw pic;

%label the graphs
label.top(btex $y=\sqrt{x}$ etex, (5ux,3uy));
label.bot(btex $y=-\sqrt{x}$ etex, (5ux,-3uy));

%xtick marks
for k=xmin step 1 until xmax:
 xtick((k*ux,0))
endfor;

%label xticks
label.bot(btex $-5$ etex, (xmin*ux,0));
label.bot(btex $5$ etex, (xmax*ux,0));

%ytick marks
for k=xmin step 1 until xmax:
 ytick((0,k*ux))
endfor;

%label xticks
label.lft(btex $-5$ etex, (0,ymin*ux));
label.lft(btex $5$ etex, (0,ymax*ux));

endfig;

beginfig(8);

%Define function to be drawn
def f(expr x)=
 -sqrt(x+2)
enddef;

%Declare and initialize viewing window
numeric xmin, xmax, ymin, ymax;
xmin=-5;
xmax=5;
ymin=-5;
ymax=5;

%Declare and initialize scaling variables
numeric ux, uy;
(xmax-xmin)*ux=2in;
(ymax-ymin)*uy=2in;

%Declare and initialize clipping boundary
path q;
q:=(xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle;
q:=q xscaled ux yscaled uy;

%Declare and initialize number of plotted points
numeric N;
N:=200;

%Declare and calculate plotting increment delta x
numeric dx;
dx:=(xmax-xmin)/N;

%Declare and create function path
path p;
p:=(-2,f(-2));
for x=-2 step dx until xmax:
 p:=p--(x,f(x));
endfor;
p:=p--(xmax,f(xmax));

%Scale function path
p:=p xscaled ux yscaled uy;

%draw the function
draw p withcolor blue;

%clip
clip currentpicture to q;

%Save and clear the function path
picture pic;
pic:=currentpicture;
clearit;

%Draw and label coordinate axes
drawdblarrow (1.1xmin*ux,0)--(1.1xmax*ux,0);
label.rt(btex $x$ etex,(1.1xmax*ux,0));
drawdblarrow (0,1.1ymin*uy)--(0,1.1ymax*uy);
label.top(btex $y$ etex,(0,1.1ymax*uy));

%Superimpose function plot
draw pic;

%xtick marks
for k=xmin step 1 until xmax:
 xtick((k*ux,0))
endfor;

%label xticks
label.bot(btex $-5$ etex, (xmin*ux,0));
label.bot(btex $5$ etex, (xmax*ux,0));

%ytick marks
for k=xmin step 1 until xmax:
 ytick((0,k*ux))
endfor;

%label xticks
label.lft(btex $-5$ etex, (0,ymin*ux));
label.lft(btex $5$ etex, (0,ymax*ux));

endfig;

beginfig(9);

%Define function to be drawn
def f(expr x)=
 -sqrt(x+2)
enddef;

%Declare and initialize viewing window
numeric xmin, xmax, ymin, ymax;
xmin=-5;
xmax=5;
ymin=-5;
ymax=5;

%Declare and initialize scaling variables
numeric ux, uy;
(xmax-xmin)*ux=2in;
(ymax-ymin)*uy=2in;

%Declare and initialize clipping boundary
path q;
q:=(xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle;
q:=q xscaled ux yscaled uy;

%Declare and initialize number of plotted points
numeric N;
N:=200;

%Declare and calculate plotting increment delta x
numeric dx;
dx:=(xmax-xmin)/N;

%Declare and create function path
path p;
p:=(-2,f(-2));
for x=-2 step dx until xmax:
 p:=p--(x,f(x));
endfor;
p:=p--(xmax,f(xmax));

%Scale function path
p:=p xscaled ux yscaled uy;

%draw the function
draw p withcolor blue;

%draw the line y=x
draw (-5u,-5u)--(5u,5u) withcolor black;

%draw the reflection
draw p reflectedabout ((0,0),(1,1)) withcolor red;

%clip
clip currentpicture to q;

%Save and clear the function path
picture pic;
pic:=currentpicture;
clearit;

%Draw and label coordinate axes
drawdblarrow (1.1xmin*ux,0)--(1.1xmax*ux,0);
label.rt(btex $x$ etex,(1.1xmax*ux,0));
drawdblarrow (0,1.1ymin*uy)--(0,1.1ymax*uy);
label.top(btex $y$ etex,(0,1.1ymax*uy));

%Superimpose function plot
draw pic;

%xtick marks
for k=xmin step 1 until xmax:
 xtick((k*ux,0))
endfor;

%label xticks
label.bot(btex $-5$ etex, (xmin*ux,0));
label.bot(btex $5$ etex, (xmax*ux,0));

%ytick marks
for k=xmin step 1 until xmax:
 ytick((0,k*ux))
endfor;

%label xticks
label.lft(btex $-5$ etex, (0,ymin*ux));
label.lft(btex $5$ etex, (0,ymax*ux));

%Label f
label.bot(btex $f$ etex, (5ux,-3uy));

%label f^-1
label.lft(btex $f^{-1}$ etex, (-3ux,5uy));

%label y=x
label.urt(btex $y=x$ etex, (5u,5u));

endfig;

beginfig(10);

%initialize scale
numeric u;
10u=2in;

%axes
drawdblarrow (-3.1u,0)--(7.1u,0);
drawdblarrow (0,-5.1u)--(0,5.1u);

endfig;

end