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Visualize or graph a function—Wolfram Documentation

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• See Also
  • ListLinePlot
  • DiscretePlot
  • ParametricPlot
  • LogPlot
  • LogLinearPlot
  • LogLogPlot
  • PolarPlot
  • Plot3D
  • ContourPlot
  • AbsArgPlot
  • ReImPlot
  • Graphics
  • Show
• Related Guides
  • Function Visualization
  • Precollege Education
  • Statistical Visualization
  • Differential Equations
  • System Model Analytics & Design
• Tech Notes
  • Basic Plotting
  • Options for Graphics
  • Graphics and Sound

Plot[f,{x,x_min,x_max}]

generates a plot of f as a function of x from x_min to x_max.

Plot[{f₁,f₂,…},{x,x_min,x_max}]

plots several functions f_i.

Plot[{…,w[f_i],…},…]

plots f_i with features defined by the symbolic wrapper w.

Plot[…,{x}∈reg]

takes the variable x to be in the geometric region reg.

• Plot is known as a function plot or graph of a function.
• Plot evaluates f at values of x in the domain being plotted over and connects the points {x,f[x]} to form a curve showing how f varies with x. It visualizes the curve .
• Gaps are left at any x where the f_i evaluate to anything other than real numbers or Quantity.
• The limits x_min and x_max can be real numbers or Quantity expressions.
• The region reg can be any RegionQ object in 1D.
• Plot treats the variable x as local, effectively using Block.
• Plot has attribute HoldAll and evaluates f only after assigning specific numerical values to x.
• In some cases, it may be more efficient to use Evaluate to evaluate f symbolically before specific numerical values are assigned to x.
• The following wrappers w can be used for the f_i:
• Annotation[f_i,label] provide an annotation for the f_i Button[f_i,action] evaluate action when the curve for f_i is clicked Callout[f_i,label] label the function with a callout Callout[f_i,label,pos] place the callout at relative position pos EventHandler[f_i,events] define a general event handler for f_i Highlighted[f_i,effect] dynamically highlight f_i with an effect Highlighted[f_i,Placed[effect,pos]] statically highlight f_i with an effect at position pos Hyperlink[f_i,uri] make the function a hyperlink Labeled[f_i,label] label the function Labeled[f_i,label,pos] place the label at relative position pos Legended[f_i,label] identify the function in a legend PopupWindow[f_i,cont] attach a popup window to the function StatusArea[f_i,label] display in the status area on mouseover Style[f_i,styles] show the function using the specified styles Tooltip[f_i,label] attach a tooltip to the function Tooltip[f_i] use functions as tooltips
• Wrappers w can be applied at multiple levels:
• w[f_i] wrap the f_i w[{f₁,…}] wrap a collection of f_i w₁[w₂[…]] use nested wrappers
• Callout, Labeled, and Placed can use the following positions pos:
• Plot has the same options as Graphics, with the following additions and changes: [List of all options]
• Possible settings for ClippingStyle are:
• Possible settings for PlotLayout that show single curves in multiple plot panels include:
• "Column" use separate curves in a column of panels "Row" use separate curves in a row of panels {"Column",k},{"Row",k} use k columns or rows {"Column",UpTo[k]},{"Row",UpTo[k]} use at most k columns or rows
• With the default settings Exclusions->Automatic and ExclusionsStyle->None, Plot breaks curves at discontinuities and singularities it detects. Exclusions->None joins across discontinuities and singularities.
• Exclusions->{x₁,x₂,…} is equivalent to Exclusions->{x==x₁,x==x₂,…}.
• Possible highlighting effects for Highlighted and PlotHighlighting include:
• Highlight position specifications pos include:
• x, {x} effect at {x,y} with y chosen automatically {x,y} effect at {x,y} {pos₁,pos₂,…} multiple positions pos_i
• PlotLegends->"Expressions" uses the f_i as the legend text.
• Plot initially evaluates f at a number of equally spaced sample points specified by PlotPoints. Then it uses an adaptive algorithm to choose additional sample points, subdividing a given interval at most MaxRecursion times.
• Since only a finite number of sample points are used, it is possible for Plot to miss features of f. Increasing the settings for PlotPoints and MaxRecursion will often catch such features.
• Themes that affect curves include:
• The arguments supplied to functions in MeshFunctions and RegionFunction are x, y. Functions in ColorFunction are by default supplied with scaled versions of these arguments.
• Possible settings for ScalingFunctions include:
• s_y scale the y axis {s_x,s_y} scale x and y axes
• Each scaling function s_i is either a string "scale" or {g,g^-1}, where g^-1 is the inverse of g.

Plot a function:

Plot several functions with a legend:

Label each curve:

Fill below a curve:

Fill between two curves:

Plot multiple filled curves, automatically using transparent colors:

More points are sampled when the function changes quickly:

The plot range is selected automatically:

Ranges where the function becomes nonreal are excluded:

The curve is split when there are discontinuities in the function:

Use Exclusions->None to draw a connected curve:

Use PlotPoints and MaxRecursion to control adaptive sampling:

Use PlotRange to focus in on areas of interest:

The domain can be specified by a region:

Specify a domain using a MeshRegion:

Plot over an infinite domain:

Use ScalingFunctions to scale the axes:

Label curves with Labeled:

Place the labels relative to the curves:

Label curves with PlotLabels:

Place the label near the curve at an value:

Use a scaled position:

Specify the text position relative to the point:

Label curves automatically with Callout:

Place a label with specific locations:

Include legends for each curve:

Use Legended to provide a legend for a specific curve:

Use Placed to change the legend location:

Curves usually have interactive callouts showing the coordinates when you mouse over them:

Including specific wrappers or interactions such as tooltips turns off the interactive features:

Choose from multiple interactive highlighting effects:

Use Highlighted to emphasize specific points in a plot:

Highlight multiple points:

Multiple curves are automatically colored to be distinct:

Provide explicit styling to different curves:

Include a legend:

Add labels for the axes and overall plot:

Add labels for the curves:

Label positions along a curve:

Provide an interactive Tooltip for each curve:

Create filled plots:

Use a plot theme:

Create an overlay mesh:

Style the curve segments between mesh points:

Plot over an infinite domain with automatic ticks:

Show multiple curves in a row of separate panels:

Use a column instead of a row:

Use multiple rows or columns:

Choose the ratio of height to width from the actual plot values:

Draw no axes:

Draw the axis but no axis:

Use labels based on variables specified in Plot:

Specify a label for each axis:

Determine where the axes cross automatically:

Specify the axes origin at the point :

Change the style for the axes:

Specify the style of each axis:

Use different styles for the ticks and the axes:

Use different styles for the labels and the axes:

Align graphs by the axis in each plot:

Omit clipped regions of the plot:

Show the clipped regions like the rest of the curve:

Show clipped regions with red lines:

Show clipped regions as red at the bottom and thick at the top:

Show clipped regions as red and thick:

Color by a scaled coordinate and scaled coordinate, respectively:

Color with a named color scheme:

Color a curve red when its absolute coordinate is above 0:

Fill with the color used for the curve:

ColorFunction has higher priority than PlotStyle for coloring the curve:

No argument scaling on the left; automatic scaling on the right:

Color a curve red when its absolute coordinate is above 0:

Use hue to indicate direction and brightness to indicate amplitude:

This inserts the graphics object in the resulting graphic:

Insert special markers to indicate whether a point belongs to the curve or not:

Find the list of values sampled by Plot:

Show where Plot evaluates Sin[x]:

Count how many times the function is evaluated:

Use automatic methods for computing exclusions, in this case for a piecewise function:

In this case, the exclusion comes from a branch cut discontinuity:

Indicate that no exclusions should be computed:

Exclude a fixed set of points:

Give a set of exclusions as an equation:

This gives two sets of exclusions:

Exclude an equation and the automatically chosen points:

Use dashed lines to indicate the vertical asymptotes:

Use black points to highlight the exclusions:

Use symbolic or explicit values:

By default, overlapping fills combine using opacity:

Fill between curve 1 and the axis:

Fill between curves 1 and 2:

Fill between curves 1 and 2 with a specific style:

Fill between curves 1 and with yellow:

Fill between curves 1 and 2; use yellow when 1 is below 2 and green when 1 is above 2:

Use different fill colors:

Fill with opacity 0.5 orange:

Fill with red below the axis and blue above:

Use a variable filling style obtained from a ColorFunction:

Use named sizes such as Tiny, Small, Medium and Large:

Specify the width of the plot:

Specify the height of the plot:

Allow the width and height to be up to a certain size:

Specify the width and height for a graphic, padding with space if necessary:

Setting AspectRatioFull will fill the available space:

Use ImageSizeFull to fill the available space in an object:

Specify the image size as a fraction of the available space:

Textual labels are shown at their actual sizes:

Image labels are automatically resized:

Specify a maximum size for textual labels:

Specify a maximum size for image labels:

The default sampling mesh:

Each level of MaxRecursion will subdivide the initial mesh into a finer mesh:

Show the initial and final sampling meshes:

Use 20 mesh levels evenly spaced in the direction:

Use an explicit list of values for the mesh in the direction:

Use a mesh evenly spaced in the and directions:

Show 5 mesh levels in the direction (red) and 10 in the direction (blue):

Color the mesh the same color as the plot:

Use a red mesh in the direction:

Use a red mesh in the direction and a blue mesh in the direction:

Use big, red mesh points in the direction:

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

Plots have interactive coordinate callouts with the default setting PlotHighlightingAutomatic:

Use PlotHighlightingNone to disable the highlighting for the entire plot:

Use Highlighted[…,None] to disable highlighting for a single curve:

Move the mouse over a curve to highlight it using arbitrary graphics directives:

Move the mouse over the curve to highlight it with a ball and label:

Use a ball and label to highlight a specific point on the curve:

Move the mouse over the curve to highlight it with a label and droplines to the axes:

Use a ball and label to highlight a specific point on the curve:

Move the mouse over the plot to highlight it with a slice showing values corresponding to the position:

Highlight the curves at a fixed value:

Move the mouse over the plot to highlight it with a slice showing values corresponding to the position:

Highlight the curves at a fixed value:

Use a component that shows the points on the curve closest to the position of the mouse cursor:

Specify the style for the points:

Use a component that shows the coordinates on the curve closest to the mouse cursor:

Use Callout options to change the appearance of the label:

Combine components to create a custom effect:

Add an overall label to the plot:

Specify text to label curves:

Place the labels above the curves:

Place the labels differently for each curve:

PlotLabels->"Expressions" uses functions as curve labels:

Use callouts to identify the curves:

Use None to not add a label:

Place each curve in a separate panel using shared axes:

Use a row instead of a column:

Use multiple columns or rows:

Prefer full columns or rows:

No legends are used by default:

Create a legend based on the functions:

Create a legend with placeholder text:

Create a legend with specific labels:

PlotLegends picks up PlotStyle values automatically:

Use Placed to position legends:

Place legends inside:

Use LineLegend to modify the appearance of the legend:

Use more initial points to get a smoother curve:

Show the curve over the whole domain:

Show the curve only where it is real valued:

Show the curve from to over the whole domain:

Constrain the curve to the framed region:

Draw the curve using the whole graphical region:

Use a theme with simple ticks and grid lines in a bright color scheme:

Change the color scheme:

Show the curve where :

Exclude the region where :

By default, plots have linear scales in each direction:

Use a log scale in the direction:

Use a linear scale in the direction that shows smaller numbers at the top:

Use a reciprocal scale in the direction:

Use different scales in the and directions:

Reverse the axis without changing the axis:

Use a scale defined by a function and its inverse:

Positions in Ticks and GridLines are automatically scaled:

PlotRange and AxesOrigin are automatically scaled:

Evaluate functions using machine-precision arithmetic:

Evaluate functions using arbitrary-precision arithmetic:

Compare several functions:

A function and its inverse are reflections in :

Illustrate that -Abs[x]≤x Sin[1/x]≤Abs[x] in the interval:

Curves are broken where a function has singularities:

Emphasize the singularities by specifying ExclusionsStyle:

Highlight the discontinuities in a function using ExclusionsStyle:

The discontinuities are automatically derived but can also be specified:

Highlight zeros of a function :

The second argument passed to MeshFunctions is :

Highlight local extrema for a function using MeshFunctions:

Local extrema are given by :

Highlight the local maximums and minimums of a function :

The local maximums are the points where and :

Similarly the local minimums are given by and :

Highlight the non-negative and non-positive parts of a function :

Using the Filling specification allows this to be readily achieved:

Highlight the segments where the function is increasing or decreasing:

A function is increasing when :

A function is decreasing when :

Show them together and add a legend:

Highlight the parts where a function is convex or concave:

A function is convex when :

A function is concave when :

Show them together with a legend:

Use color to overlay the derivative of function on top of the curve for :

By rescaling the derivative to be between 0 and 1, you can easily map to a color:

From ColorData you can get a variety of color scales:

The derivative can now be overlaid as color on top of the curve using ColorFunction:

Using Filling emphasizes the color more:

The epigraph of a function is given by . You can visualize the epigraph by using Filling:

The hypograph of a function is given by . You can visualize the hypograph by using Filling:

Plot the real and imaginary parts of a complex-valued function of a real variable:

Plot the magnitude and phase of a complex-valued function of a real variable:

Plot the magnitude and color based on the phase of the function:

Add filling and a color legend that provides a separate axis for the phase:

The general solution to a differential equation:

Plot two particular solutions:

Plot a family of solutions:

The general solution to an algebraic equation:

Plot a family of solutions:

Eigenfunctions in a potential well:

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