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:
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 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 the "Graph It!"
button
each
time
a new or modified expression is given in order to have it
effective before using 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. Enter any functions in the text inputs and click 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 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 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 (see 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 bound From and upper bound To are provided.
Length Button (see demo)
To compute the length of the arc of f(x) between two
points
along a curve, enter the limit values for "From"
and
"To" on its text fields, then
click the Find Length button.
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. If a maxima or a minima value is found when
clicked, it shows the 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. 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 displayed on the
labels marked x = and f(x)
=. This option also implies to find the roots of the
equation
f(x) = 0.
Tangent/Normal
To find the tangent or normal line to f(x) at a
given point
x, click the Tangent button to
display the Add Tangent/Normal
dialog. Enter a value of x
and then click the OK button.
In addition, the dynamic tangent line is shown while
clicking 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, and the Numerical
Computation of Series
dialog is displayed. From this popup dialog enter a series
expression, the values of Start, End and in steps of.
Click
the
Compute Sum
button.
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 the Solve button.
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. For other
coordinates, use "t" as the
input variable of Polar function r(t) or
Parametric functions x(t), y(t).
View 3D
Select the View
3D mode, it displays a 3D graph in
the three dimensional
coordinates in which its motion by default is shown. Click 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. Enter the values of lower bound From and upper bound To. Click the Volume
or Surface Area
button.
Gamma
Computation  Compute a Value of Gamma Function
Select Gamma
Function
item from Math Utilities
menu. Enter a
value for x and then click the Gamma
Computation
button.
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.
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.
Notes
When you access this website or
click on a GraphFunc hyperlink in this
page, the GraphFunc tool (applet) will be
automatically displayed in the popup
window. 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.
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@seriesmathstudy.com .
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