Note the use of the semicolon (;) to suppress intermediate graphics from being plotted.

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Plot has a variety of options that can be viewed by typing Plot or Options[Plot]. These options may be used individually or in conjunction with one another. Some of the more common options are described in the remainder of this section. Since Mathematica obviously cannot plot an infinite number of points, it selects a finite number of equally spaced points as sample points and uses an adaptive algorithm to construct a smoothlooking curve. The initial number of points it will use, PlotPoints, is set to 50 by default. If the curve wiggles excessively, a larger number might be necessary to obtain a smooth-looking curve.

PlotPoints n specifies that an initial number of n sample points should be used in the construction of the graph. MaxRecursion n specifies that up to n levels of recursion should be made in the adaptive algorithm. Recursive subdivision is done only in those places where more samples seem to be needed in order to achieve results with a certain level of quality.

When you plot a graph, you will notice that the horizontal and vertical axes are usually not the same length. By default, the ratio of vertical axis length to horizontal axis length is 1/GoldenRatio, where GoldenRatio = (1 + 5 ) / 2 . The designers of Mathematica felt that this ratio was the most comfortable and pleasing to the eye. It can be changed with the option AspectRatio, which determines the height-to-width ratio of the graph.

AspectRatio Automatic computes the aspect ratio from the actual coordinate values of the plot. AspectRatio ratio sets the ratio of height to width to the value ratio.

Two-Dimensional Graphics

EXAMPLE 7

Plot[x2, {x, 5, 5}]

Plot[x2, {x, 5, 5}, AspectRatio Automatic]

25 20 15 10 5 4 2 2 4 4 2 2 4 5

Both axes are scaled identically.

EXAMPLE 8 The following command should produce a circle of radius 3 centered at the origin. However, because of unequal axis scaling, the graph appears as an ellipse.

Plot[{ Sqrt[9 x2], Sqrt[9 x2]}, {x, 3, 3}]

3 2 1 3 2 1 1 2 3 1 2 3

Two-Dimensional Graphics

We can make the circle appear round by setting AspectRatio Automatic. Plot[{ Sqrt[9 x2], Sqrt[9 x2]}, {x, 3, 3}, AspectRatio Automatic]

When graphing a function, Mathematica makes a calculated decision where to place the origin. If (0, 0) is within the plotting region, the axes will cross at that location. If not, an algorithm decides where the axes should cross. This can sometimes lead to a confusing (and misleading) rendering of the function. The option AxesOrigin gives control over the placement of the intersection point.

AxesOrigin Automatic is the default. If the point (0, 0) is within, or close to, the plotting region, then it is usually chosen as the axis origin. AxesOrigin {x, y} forces the intersection of the axes to be the point (x, y).

EXAMPLE 9

Plot[5 + x4, {x, 1, 2}]

20 18 16 14 12 10 8 1.2 1.4 1.6 1.8 2.0

The axes intersect at (1, 6). The graph is drawn completely, however, from x = 1 to x = 2.

Two-Dimensional Graphics

Plot[5 + x4, {x, 1, 2}, AxesOrigin {0, 0}]

When multiple graphs are drawn on the same set of axes, Mathematica distinguishes them by color. PlotStyle allows the user to alter the appearance of a graph in other ways using style options.

PlotStyle style if only one style option is used. PlotStyle {style1, style2, . . .} if several style options are desired. If more than one graph is to be modified, the styles are applied cyclically.

Some of the more common style options are listed in the following:

GrayLevel[x] for 0 x 1 allows lightening of the image. The closer x is to 1, the lighter the image will appear.