Examples for

Plotting & Graphics

Plotting and graphing are methods of visualizing the behavior of mathematical functions. Use Wolfram|Alpha to generate plots of functions, equations and inequalities in one, two and three dimensions. Gain additional perspective by studying polar plots, parametric plots, contour plots, region plots and many other types of visualizations of the functions and equations of interest to you.

Functions

Graph a function of one variable as a curve in the plane.

Plot a function of one variable:

plot x^3 - 6x^2 + 4x + 12
graph sin t + cos (sqrt(3)t)
plot 4/(9*x^(1/4))

Specify an explicit range for the variable:

plot e^x from x=0 to 10

Plot a real‐valued function:

real plot -(sqrt(25-y^2))

Plot a special function:

plot Ai(x)

Plot several functions:

plot sin x, cos x, tan x
plot x e^-x, x^2 e^-x, x=0 to 8

Plot a function on a logarithmic scale:

log plot e^x-x

Plot on a log-linear scale:

log-linear plot x^2 log x, x=1 to 10

Equations

Plot the solution set of an equation in two or three variables.

Plot the solution to an equation in two variables:

plot 3x^2-2xy+y^2=1

Plot a quadric surface:

plot x^2 - 3y^2 - z^2 = 1

Parametric Plots

Graph parametric equations in two or three dimensions.

Draw a parametric plot:

parametric plot (cos^3 t, sin^3 t)

Specify a range for the parameter:

parametric plot (sin 10t, sin 8t), t=0..2pi

Draw a parametric curve in three dimensions:

3d parametric plot (cos t, sin 2t, sin 3t)

Draw a parametric surface in three dimensions:

3d parametric plot (cos u, sin u + cos v, sin v), u=0 to 2pi, v=0 to 2pi

3D Plots

Plot a function of two variables as a surface in three-dimensional space.

Plot a function in two variables:

plot sin x cos y

Specify explicit ranges for the variables:

plot x^2 y^3, x=-1..1, y=0..3

Inequalities

Plot the solution set of an inequality or system of inequalities.

Plot the region satisfying an inequality in two variables:

plot |x|^3+|y|^3<1

Plot a region satisfying multiple inequalities:

plot x^2+y^2<1 and y>x
Number Lines

Plot a set of numbers or values on a real number line.

Visualize a set of real numbers on a number line:

number line 2, 3, 5, 7, 11, 13

Show multiple sets on a number line:

number line x^2>5, 0<=x<3
More examples

RELATED EXAMPLES

  • Algebra
  • Applications of Calculus
  • Domain & Range
  • Geometry
  • Numbers

    • Polar Plots

    Draw a graph of points or curves in the polar coordinate system.

    Draw a polar plot:

    polar plot r=1+cos theta

    Specify a range for the variable theta:

    polar plot r=theta, theta=0 to 8 pi