Start GraphFunc
(Java
Runtime Environment required)
The GraphFunc tool (beta version) is a program online that is used to plot the graph of mathematical functions in two or three coordinate systems and help exploring several topics in calculus. It has the following features:
When you access this website or click on a GraphFunc hyperlink in this page, the GraphFunc tool (applet) will be displayed in the popup window that you can use to graph your functions online. If your browser does not display GraphFunc, check whether you need to download JRE (Java Runtime Environment) from Sun or setup your browser security in secure default configuration. (Try the new GraphFunc version if your computer has JRE 1.5x or 1.6x.)
How to use GraphFunc tool
Use "Graph It!"
Button To Plot A Graph
Enter a function f(x) in the text input (or command line)
marked “f(x) = ”. Then click on the Graph It! button to draw the graph in 2D Cartesian
coordinates (by default). The graph can be moved or dragged to any
positions. Always click on the "Graph It!"
button each time a new or modified expression is given in order to have it
effective before using any other buttons.
Cartesian, Polar or Parametric Coordinates Mode (see demo)
The option under the Cartesian dropdown list box helps User to plot the
function(s) in Polar or Parametric coordinates. Use x as the input variable of
f(x) in twodimensional Cartesian coordinates, and x, y as the variables of z
= f(x, y) in threedimensional Cartesian coordinates. For the
Polar and Parametric coordinates, t is used
as the input variable of f(t).
Single/Multiple Graph  Plot Multiple Graphs Synchrnous
Want to plot two or more graphs synchronous. Need to
switch to Multiple Graph mode by selecting the Multiple Graph item from the Single
Graph dropdown list box. After switching to Multiple Graph mode, a list of the text inputs is
displayed. Then enter any functions in the text inputs and click on the Graph It button to see its graphs. A current
active function is indicated by a red indicator marked on f1(x) =
, f2(x) = , ...or f5(x) =.
To turn a function to be an active, click with the mouse on either a text field
or its function label. For example, if there are five functions entered
in text fields and the user wants to compute the area under the curve f3(x).
First, click on the text field marked "f3(x) =
" to make sure the red indictor is displayed. Second, provide the
values of the lower and upper bounds then click on the Find
Area button to get the result. The behavior of this example can be
applied to other computing functionalies such as
volume, tangent, extremum, xintercepts, and
derivatives.
Calc Buttons  Compute f and Its First & Second Derivative at a Given Point
The values of f(x1), f '(x1) (first derivative) and f "(x1) (second derivative) at a given
point x1 can be computed by clicking on the Calc
button in Cartesian coordinates. These values can be also determined when
clicking with the mouse at any points on the graph. This feature is
applied to the Polar and Parametric coordinates in which its variable is
denoted "t". When in
either Polar or Parametric coordinates mode, there are two Calc buttons: one is used for compution
in terms of variable t; the other is used
for computation in terms of variable x.
Area Button  Compute Area Under A Curve (click here
to see a demo)
The area under a graph in 2D (not 3D) Cartesian coordinates
is computed by clicking on the Find Area
button right after the values of the lower (label marked "From") and upper bounds (label marked "To") are provided.
Length Button (click here to
see a demo)
To compute the length of the arc of f(x) between two points
along a curve, enter the "From" and
"To" values on its text fields, then
click on the Find Length button to get the
result.
Maxima or Minima (Extremum)
To find a local maxima or minima of
function f(x), select the Extremum item from the Functions dropdown
list box. Then click on the graph at any points near to the vertices to
get the computed results. If a maxima or a minima value is found when
clicked, it shows the computed results onto the text field at the label marked x = and f(x) = .
XIntercept
To find the xintercepts where f(x) or y = 0, choose the Xintercept item from the Functions
dropdown list box, and then click on the graph at some points where f(x)
nearly crosses the xaxis. If a value of x as f(x) approaches to 0 is
found, its result is computed and displayd onto the
labels marked x = and f(x)
=. This option also implies to find the roots of the equation when
f(x) = 0.
Tangent/Normal
To find the tangent or normal line to f(x) at a given point
x, click on the Tangent button to display the Add Tangent/Normal dialog. Enter a value of x
and then click on the OK button to see the
result. In addition, the dynamic tangent line is shown while
clicking with the mouse on any points on the graph or dragging it along the
horizontal xaxis.
Sum Series
GraphFunc has a capability of
computing the sum of a series up to nth
terms. To use this functionality, select the Sum
Series item from the Functions dropdown
list to display the Numerical Computation of Series
dialog. From this popup dialog enter a series expression in the command
line, and provide the values in the textfields with
labels marked Start, End and in steps of
, which represent the first
term, the last term and the stepwidth of the series, respectively.
Afterwards, click on the Compute Sum button
to get the sum.
System of Linear Equations
Want to solve a System of
Linear Equations with n equations and n
unknowns. Select the Linear Equations item from the Functions dropdown list, a window with four equations and four
unknowns (by default) is displayed. From this window enter the
coefficient values of equations in the text fields then click on the Solve button to get the
result.
View 2D
The View 2D dropdown list
box is used to switch the graph(s) from 2D to 3D or vice versa. The
graph(s) can be plotted in Cartesian, Polar or Parametric coordinates by
selecting an item under Cartesian dropdown list
box. Currently, GraphFunc supports two variables
x and y as variables of function z = f(x,y)
in threedimensional Cartesian coordinates. Use "t" as the input variable of Polar function r(t) or Parametric functions x(t), y(t) in the Polar or
Parametric coordinates.
View 3D
Select the View 3D mode, it displays a graph in the three dimensional
coordinates in which its motion by default is shown. Click on the Motion checkbox to turn it on or off.
Volume or Surface Area Button
Select the xaxis item
from the Rotation dropdown list box to rotate
the graph around the xaxis. Click on the Volume
or Surface Area button to compute the
volume or the surface area generated from this revolution after the values of
the lower bound (label marked "From") and the
upper bound (label marked "To") are provided.
Gamma
Computation  Compute a Value of Gamma Function
Select Gamma Function
item from Math Utilities menu. Enter a
value for x and then click on the Gamma Computation
button to get the result.
Zoom In / Out Button
A graph can be zoomed in or out when clicking on the Zoom In or Zoom Out
button.
Reset Button
Clicking on the Reset
button is to clear data and reset the GraphFunc
tool's configuration to its default values.
(Note: The below instructions are applied to the new and old GraphFunc versions. However, some are not applied to the old version.)
Some examples
Twodimensional plotting functions 
Enter f(x) = 
xsin(x) 
x*sin(x) (enter this function into command line) 
x^3 +x 1 

(x^3 + x + 4)/(x  1) 

(sin(x))^3 + cos(x) 



Threedimensional
plotting functions 
Enter f(x,y) = 
z = f(x,y) = sin(x+y) 
sin(x+y) 
x^2 + y^2  3 

exp(x) + sin(y) or e^x + sin(y) 



Polar Graphs (2D) 
Select the Polar item from the Cartesian dropdown listbox, then enter 
6/(6  5*sin(t)) 

sin(5*t) 

(Butterfly Curve) 
e^(cos(t))  2*cos(4*t) + sin(t/12)^5 


Parametric Graphs
(3D) 
Select the Parametric item from the Cartesian dropdown list, then enter 
sin(t) + 2*cos(t)
(into the text field with label marked f1(t) = ) 

cos(t) 
(More functions and examples...)
Now choose a function and use GraphFunc tool as shown above or click here to graph it.
My fellow Americans: ask not what your country can do for you – ask what you can do for your country. 
John F. Kennedy 
Thank you for using GraphFunc online. Any suggestions and comments are welcome to sms_century21@seriesmathstudy.com .
This website is sponsored by www.seriesmathstudy.com.