> plot( [(x^3+1)/x, x^2], x=-3..3, y=-9..9,

color=[red,blue], thickness=3,

style=[line,point], symbol=point,

numpoints=100, scaling=unconstrained );

 

 

 


 

# Program: sketch y=f(x) and see all its bends (turns)

> draw := proc()

local f,type,soln,n,i,j,r,m,M,d;

 

m :=  10^10;

M := -10^10;

printf("Enter a function in terms of x:\n");

f := scanf("%a")[1];

type := [ solve(f,x) ];

for i from 1 to nops(type) do

  soln := [ evalf( allvalues( type[i],'independent' ) ) ];

  #print(soln);

  n := nops( soln );

  printf("type %d: # soln= %d, real part:", i,n);

  for j from 1 to n do

    r := Re( evalf(soln[j]) );

    printf(" %f,",r);

    if r > M then M := r; fi;

    if r < m then m := r; fi;

  od;

  printf("\n");

od;

if M>m then d:=(M-m)/4; else d:=5; fi;

printf("m=%f, d=%f, M=%f\n", m,d,M );

printf("X-range: %f .. %f\n", m-d,M+d );

plot(f,x=m-d..M+d);

  end:

 

# Execute the program:

> draw();

Enter a function in terms of x:

> x^5-x^3+x-1

type 1: # soln= 1, real part: 1.000000,

type 2: # soln= 4, real part: .518913, .518913, -1.018913, -1.018913,

m=-1.018913, d=.504728, M=1.000000

X-range: -1.523641 .. 1.504728

 

 

 


 

# Program: show graphs of functions in the same view rectangle

> sin2i := proc()

local pic, i, n;

with(plots);

printf("Enter n to see graphs of {y=sin(x)^i, x=0..Pi} for i=1 to n:\n");

n := scanf("%d")[1];

for i from 1 to n do

  pic[i] := plot(sin(x)^i, x=0..Pi);

od;

display( [ pic[j] $j=1..n ] ); # j cannot be declaired!

end:

 

# Execute the program:

> sin2i();

Enter n to see graphs of {y=sin(x)^i, x=0..Pi} for i=1 to n:

> 20