# Options for Graphics

When

*Mathematica* plots a graph for you, it has to make many choices. It has to work out what the scales should be, where the function should be sampled, how the axes should be drawn, and so on. Most of the time,

*Mathematica* will probably make pretty good choices. However, if you want to get the very best possible pictures for your particular purposes, you may have to help

*Mathematica* in making some of its choices.

There is a general mechanism for specifying "options" in

*Mathematica* functions. Each option has a definite name. As the last arguments to a function like

Plot, you can include a sequence of rules of the form

, to specify the values for various options. Any option for which you do not give an explicit rule is taken to have its "default" value.

Plot[f,{x,x_{min},x_{max}},option->value] |

| make a plot, specifying a particular value for an option |

Choosing an option for a plot.

A function like

Plot has many options that you can set. Usually you will need to use at most a few of them at a time. If you want to optimize a particular plot, you will probably do best to experiment, trying a sequence of different settings for various options.

Each time you produce a plot, you can specify options for it.

"Redrawing and Combining Plots" will also discuss how you can change some of the options, even after you have produced the plot.

Some of the options for Plot. These can also be used in Show.

Here is a plot with all options having their default values.

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This draws axes on a frame around the plot.

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This specifies labels for the

and

axes. The expressions you give as labels are printed just as they would be if they appeared as

TraditionalForm *Mathematica* output. You can give any piece of text by putting it inside a pair of double quotes.

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You can give several options at the same time, in any order.

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Setting the

AspectRatio option changes the whole shape of your plot.

AspectRatio gives the ratio of width to height. Its default value is the inverse of the Golden Ratio—supposedly the most pleasing shape for a rectangle.

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Some common settings for various options.

When

*Mathematica* makes a plot, it tries to set the

and

scales to include only the "interesting" parts of the plot. If your function increases very rapidly, or has singularities, the parts where it gets too large will be cut off. By specifying the option

PlotRange, you can control exactly what ranges of

and

coordinates are included in your plot.

Automatic | show at least a large fraction of the points, including the "interesting" region (the default setting) |

All | show all points |

{y_{min},y_{max}} | show a specific range of values |

{xrange,yrange} | show the specified ranges of and values |

Settings for the option PlotRange.

The setting for the option

PlotRange gives explicit

limits for the graph. With the

limits specified here, the bottom of the curve is cut off.

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*Mathematica* always tries to plot functions as smooth curves. As a result, in places where your function wiggles a lot,

*Mathematica* will use more points. In general,

*Mathematica* tries to

*adapt* its sampling of your function to the form of the function. There is a limit, however, which you can set, to how finely

*Mathematica* will ever sample a function.

The function

wiggles infinitely often when

.

*Mathematica* tries to sample more points in the region where the function wiggles a lot, but it can never sample the infinite number that you would need to reproduce the function exactly. As a result, there are slight glitches in the plot.

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It is important to realize that since

*Mathematica* can only sample your function at a limited number of points, it can always miss features of the function.

*Mathematica* adaptively samples the functions, increasing the number of samples near interesting features, but it is still possible to miss something. By increasing

PlotPoints, you can make

*Mathematica* sample your function at a larger number of points. Of course, the larger you set

PlotPoints to be, the longer it will take

*Mathematica* to plot

*any* function, even a smooth one.

More options for Plot. These cannot be used in Show.

This uses

PlotStyle to specify a dashed curve.

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When plotting multiple functions,

PlotStyle settings in a list are used sequentially for each function.

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When a

PlotStyle contains a sublist, the settings are combined.

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By default nothing is indicated when the

PlotRange is set, so that it cuts off curves.

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Setting

ClippingStyle to a list defines the style for the parts cut off at the bottom and top.

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This specifies filling between the curve and the

axis.

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The filling can be specified to extend to an arbitrary height, such as the bottom of the graphic. Filling colors are automatically blended where they overlap.

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This specifies a specific filling to be used only for the first curve.

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This shows a filling from the first curve to the second using a nondefault filling style.

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