(*^

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                                           Vector-Valued Functions

The cell below shows how a vector-valued function can be defined in Mathematica.  Evaluate it now. 
;[s]
6:0,1;66,0;136,2;147,0;150,3;165,0;168,-1;
4:3,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,0,0,0;1,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
Clear[f, g, h]

f[t_] := {t - 1, 2t + 1}

f[1]

g[t_] := {Cos[t], Sin[t], t}

g[Pi]

h[t_] := {2, 3 t + 3, 5 t + 6, 3 t - 2}

h[3]
:[font = special1; inactive; preserveAspect; ]
The cell below shows how Mathematica  can graph a vector-valued function whose values are in R^2 using the ParametricPlot procedure.  This particular example shows the travels of a baseball thrown from an initial height of 5 feet with an initial velocity of 30 feet per second horizontally and 30 feet per second vertically.

Notice the syntax.  The x-coordinate and the y-coordinate of the baseball's travels are denoted by
Baseball[t][[1]] and Baseball(t)[[2]] respectively and are enclosed in set brackets.  

Evaluate the next cell now.  

Notice that the baseball doesn't quite reach the ground because the range for the time variable, t, is not quite long enough.
;[s]
13:0,0;25,1;36,0;107,2;121,0;425,2;441,0;446,2;462,0;513,3;539,0;640,2;642,0;670,-1;
4:7,13,9,Times,0,12,0,0,0;1,13,9,Times,2,12,0,0,0;4,13,9,Times,1,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
Clear[Baseball]

Baseball[t_] := {30 t, 5 + 30 t - 16 t^2}

ParametricPlot[{Baseball[t][[1]], Baseball[t][[2]]},
               {t, 0, 2}]
^*)