3.2 Plotting a Function

We begin with a simple example:

  In[1]:= <b class="bold">Clear[f];</b><b class="bold">              f[x_] := x</b><sup<b class="bold">2</b></sup><b class="bold"> <span class="unicode">?</span></b> <b class="bold">2x + 4</b>  In[3]:= <b class="bold">Plot[f[x], {x, <span class="unicode">?</span>1, 3}]</b><span class="inlinemediaobject"><a NAME="IMG_86"> href="portalcontent.asp?bkid=31099&image_src=https://images.books24x7.com/bookimages/id_31099/fig66%5F01%5F0%2Ejpg&image_id=86&previd=IMG_86"> target="_parent"><img alt="Image from book"> border="0"> height="162"> id="IMG_86"> src="https://images.books24x7.com/bookimages/id_31099/fig66_01.jpg"> title="Click To expand"> width="290"></a></span>

The Plot command takes two arguments, separated (as always) by a comma. The first (in this case f[x]) is the function to be graphed, and the second (in this case {x, -1, 3}) is called an iterator. It describes the span of values that the variable x is to assume; that is, it specifies the domain over which the plot will be constructed. The curly brackets are essential in describing this domain. In fact, Mathematica uses this iterator structure in numerous commands, so it warrants a bit of discussion. The first item ( x) names the variable, and the next two items give the span of values that this variable will assume ( ?1 through 3). Values in this domain are displayed along the horizontal axis, while the values that the function assumes are displayed along the vertical axis.

Note that the axes in this plot do not intersect at the origin, but rather at the point (0, 3). Every time you use the Plot command Mathematica decides where to place the axes, and they do not...