GraphFunc Online
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(Start GraphFunc)
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:
- Plotting the elementary function(s) in two or three dimensional Cartesian, Polar and Parametric coordinates (see demo).
- Computing the first derivative and second derivative of f(x) in Cartesian coordinates.
- Computing the values t, x, f(t), f(x) and the first and second derivatives of these functions in Polar or Parametric coordinates.
- Computing the extreme value(s) or the maxima and minima of f(x) (see demo).
- Computing the x-intercepts where f(x) = 0.
- Computing the area under a curve (see demo).
- Computing the surface area of a solid of revolution.
- Computing the arc length of a curve between
two points (see demo).
- Computing the volume of a solid of revolution with the disc and washer methods.
- Finding the equations of tangent and normal to the curves and plotting them.
- Solving a System of Linear Equations.
- Solving an equation in one variable.
- Computing the sum of a series.
- Supporting Mortgage Calculator.
- Dragging-rotating or zooming in/out a graph.
The popup dialog is GraphFunc tool (applet) 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
(Note: The below instructions are applied to the new and old GraphFunc versions. However, some are not applied to the old version.)
Use "Graph It!" Button To Plot A Graph
Enter a function f(x) in the text input (or command line) that has its label marked as “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. Notice that user always clicks on the “Graph It!” button each time a new or modified functional expression is given into the command-line before using any other buttons. Also, the examples of using this GraphFunc tool are provided to explore several topics in Calculus as described in the above hyperlinks of this page.
Cartesian, Polar or Parametric Coordinates Mode (see demo)
The option in the Cartesian dropdown list box helps the user to plot the function(s) in Polar or Parametric coordinates. Use x as the input variable of f(x) in two-dimensional Cartesian coordinates, and x, y as the variables of z = f(x, y) in three-dimensional Cartesian coordinates. For the Polar and Parametric co-ordinates, 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. Select the Multiple Graph item from the Single Graph drop-down list box to display a list of the text inputs. Then enter any functions in the text inputs and click on the Graph It button to see its graphs. When in the Multiple Graph mode, an active function is shown with the red indicator (on the label) marked on either f1(x) = , f2(x) = , ...or f5(x) =. To turn a function to be an active by clicking with the mouse on either a text field or a function label. This indicator helps the user to compute the area or the volume or to plot the tangent of a specific function that is active. 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 or the label marked as "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, x-intercepts, 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 the 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 as "From") and upper bounds (label marked as "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 the 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 drop-down list box, then click on any of the vertices of the graph from the left panel to display the result(s). Per clicked, the maxima or minima value of f(x) (if found) is determined and displayed onto the text field and the label marked x = and f(x) = .
X-Intercept
To find the x-intercepts where f(x) or y = 0, choose the X-intercept item from the Functions dropdown list box, and then click on the graph at some points where f(x) nearly crosses the x-axis. If a value 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 x-axis.
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 step-width 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 three-dimensional 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
At the mode of View 3D, the graph is displayed in the three dimensional coordinates with the motion is shown by default. The motion is turned on or off by clicking on the Motion checkbox.
Volume or Surface Area Button
Select the x-axis item from the Rotation dropdown list box to rotate the graph around the x-axis. 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.
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.)
Use "Graph It!" Button To Plot A Graph
Enter a function f(x) in the text input (or command line) that has its label marked as “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. Notice that user always clicks on the “Graph It!” button each time a new or modified functional expression is given into the command-line before using any other buttons. Also, the examples of using this GraphFunc tool are provided to explore several topics in Calculus as described in the above hyperlinks of this page.
Cartesian, Polar or Parametric Coordinates Mode (see demo)
The option in the Cartesian dropdown list box helps the user to plot the function(s) in Polar or Parametric coordinates. Use x as the input variable of f(x) in two-dimensional Cartesian coordinates, and x, y as the variables of z = f(x, y) in three-dimensional Cartesian coordinates. For the Polar and Parametric co-ordinates, 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. Select the Multiple Graph item from the Single Graph drop-down list box to display a list of the text inputs. Then enter any functions in the text inputs and click on the Graph It button to see its graphs. When in the Multiple Graph mode, an active function is shown with the red indicator (on the label) marked on either f1(x) = , f2(x) = , ...or f5(x) =. To turn a function to be an active by clicking with the mouse on either a text field or a function label. This indicator helps the user to compute the area or the volume or to plot the tangent of a specific function that is active. 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 or the label marked as "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, x-intercepts, 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 the 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 as "From") and upper bounds (label marked as "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 the 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 drop-down list box, then click on any of the vertices of the graph from the left panel to display the result(s). Per clicked, the maxima or minima value of f(x) (if found) is determined and displayed onto the text field and the label marked x = and f(x) = .
X-Intercept
To find the x-intercepts where f(x) or y = 0, choose the X-intercept item from the Functions dropdown list box, and then click on the graph at some points where f(x) nearly crosses the x-axis. If a value 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 x-axis.
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 step-width 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 three-dimensional 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
At the mode of View 3D, the graph is displayed in the three dimensional coordinates with the motion is shown by default. The motion is turned on or off by clicking on the Motion checkbox.
Volume or Surface Area Button
Select the x-axis item from the Rotation dropdown list box to rotate the graph around the x-axis. 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.
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.
|
Two-dimensional 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) |
| Three-dimensional
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) = ) sin(2*t) (into the text field with label marked f2(t) = ) |
 |
cos(t) sin(t) |
Now
choose a function and use GraphFunc tool as shown above or click here to graph
it.
Thank you for using GraphFunc online. Any suggestions and comments are welcome to sms_century21@seriesmathstudy.com .