Plotter for Multiple(4) Types of Real Functions: Implicit, Explicit, Parametric and Polar (version 4.1)

This plotter is an combination of 4 types of real function plotters. 
It can plot 4 types of real functions: Implicit, Explicit, Parametric and Polar, on the same coordinate system.
        Implicit function: f0(x,y)=0;
        Explicit function: y=f1(x);
        Parametric function: x=g(t), y=h(t);
        Polar function: r=r(a).
It can be used for function comparison and investigation of relationships between multiple functions of different types. 

1. Click "Run/Re-Run Plotter" button to plot the pre-defined example functions.
2. Input your own function formula or change the example functions.
3. Change or set the x-y plot range [xmin, xmax] and [ymin, ymax], the t range [tmin, tmax], 
    and the a(angle) range [amin, amax], for your own functions, if needed.
4. Click "Run/Re-Run Plotter" button to plot your new/re-defined functions. 
5. The plotter is auto-scaled and auto-centered to include graphs of explicit, parametric, 
    and polar functions, but not implicit function graph.
6. For implicit function, the plotter itself can not detect the graph existence range. 
    If the existence range are not known to you beforehand, you can set
    a larger x-y plot range to catch the graph.
7. If the displayed graph is too small, you can use the mouse(left key, down-move-up) to select 
    part of the graph and the plotter will zoom-in and magnify the selected graph part automatically.
    Use "Zoom-out/Back" button to reverse the zoom-in.
8. You can add or remove one or more functions using the Checkboxes.

A more detailed usage of this function plotter is at the end of this page.

Restart/Reload This Web Page

Select Graph Plot Size:Set Width of Graph Line:

Keep Graph Shape or Not:

Click "Run/Re-Run Plotter" Button to Start

Input Your Own Function Definition or Change the Pre-defined Example
Use Checkboxes to Select Functions to Plot (Must Select at Least One Function)

Implicit Function f0(x,y):

Explicit Function f1(x):

Input X Plot Range---xmin and xmax:

Input Y Plot Range---ymin and ymax:

Parametric Function x=g(t) and y=h(t):

Input Parameter t Plot Range---tmin and tmax:

Polar Equation r=f(a):

Input Parameter a(angle) Plot Range---amin and amax (rad):

Saved Projects:

How to save your projects for later use:
Click "Save Project" to save the current project to your device. All necessary function(s) and parameters will be saved.
Click "Load Project" to load a saved project and run it.
Click "Delete Project" to remove the selected project from your device.
Note: Your projects will remain saved to your device unless you delete them or you clear the site data of your browser.

Sharing your projects:
To create a URL link for the current project, click the "Share Function" button below the graph(s).
This will copy a link containing the current project to your clipboard that you can share with others.
You can also save a PNG image of the current graph by clicking the "Save Graph as Image" button.

Disclaimer: No data saved with these tools are kept by or sent to mathonthecloud.com. Everything is saved locally to your device only.

More Usage Information for the Function Plotter:

The plotter provides a set of example functions to demo the function formula syntax, use the "Select Menu,,," to see and plot the examples.
The function input follows JavaScript syntax and support all the JavaScript Math functions, such as cos(), sin(), abs(), sqrt(), etc.. See"Supported Operators and Functions".
For function formula, supported operators are limited to: +(Addition), -(Subtraction), *(Multiplication), /(Division), and ^(or **)(Exponentiation).
Other operators, such as &, &&, |, ||, >>, >, <<, <, %, !, etc., are not supported for function formula 
and they will be treated as errors, although they are legal JavaScript operators.
When move the mouse cursor on the plotter canvas, the mouse position on the math space (x,y) will be displayed.
The plotter will catch most of user-input errors and function singularity errors, and will display a notice for possible error causes.
After correct the error, click "Run/Re-Run Plotter" button to re-run the plotter.
Plot of implicit function f0(x,y) is based on detecting sign (+/-) change of f(x,y). If f(x,y) always >=0 or always <=0, the f(x,y)=0 graph can not be plotted. For example, f(x,y)=(x^2+y^2-9)^2=0 graph can not be plotted, but f(x,y)=x^2+y^2-9=0 or f(x,y)=(x^2+y^2-9)^3=0 graph will be plotted correctly.
The plotted graph is auto-scaled and auto-centered on the canvas. If the checkbox "Keep Graph Shape or Not" is checked, the plotter uses the same scale factor in both x and y directions and the graph will keep its original shape. If the checkbox is unchecked, the graph will be stretched in one direction to make full use of the canvas area.