Function Grapher

Visualize mathematical functions in 2D and 3D with interactive graphs

2D Graph
3D Graph
Functions to Plot
Function Library

Click on a function to add it to the input field:

sin(x)
Sine
cos(x)
Cosine
tan(x)
Tangent
exp(x)
Exponential
log(x)
Natural Log
x^2
Quadratic
sqrt(x)
Square Root
abs(x)
Absolute Value
1/x
Reciprocal
sin(x)/x
Sinc Function
sin(x)*cos(y)
3D Surface
x^2 + y^2
Paraboloid
Function Graphing Knowledge
Understanding Function Graphs

Function graphs are visual representations of mathematical functions that show the relationship between inputs and outputs. They are essential tools for understanding function behavior, identifying key features, and solving mathematical problems.

Key elements of function graphs include:

  • Domain: Set of all possible input values
  • Range: Set of all possible output values
  • Intercepts: Points where the graph crosses the axes
  • Asymptotes: Lines that the graph approaches but never touches
  • Symmetry: Even, odd, or periodic properties
2D vs 3D Graphing

Function graphing can be done in both 2D and 3D:

2D Graphing
  • Plots functions of a single variable: y = f(x)
  • Shows relationship between x and y
  • Ideal for analyzing function behavior
  • Useful for finding roots, maxima, minima
3D Graphing
  • Plots functions of two variables: z = f(x,y)
  • Shows surfaces in three-dimensional space
  • Reveals contours and level curves
  • Essential for multivariable calculus

Function Grapher FAQ

Frequently asked questions about using the grapher

How do I enter a function?
Enter mathematical expressions using standard notation. For example:
  • sin(x) for sine function
  • x^2 for x squared
  • log(x) for natural logarithm
  • exp(x) for exponential function
You can use constants like pi and e.
Why is my function not plotting correctly?
Common issues include:
  • Syntax errors - ensure you're using valid mathematical expressions
  • Division by zero - avoid functions that divide by zero in your range
  • Undefined values - functions like log(x) are undefined for x ≤ 0
  • Range issues - adjust your X and Y ranges to include the function's domain
Try simplifying your function or breaking it into smaller parts.
Can I plot multiple functions at once?
Yes! You can add multiple functions by entering them one by one and clicking "Add Function". Each function will be plotted in a different color. You can remove individual functions by clicking the delete button next to each function.
What do the different point density settings do?
Point density controls how many points are calculated for each function:
  • Low: Fewer points, faster rendering for complex functions
  • Medium: Balanced approach for most functions
  • High: More points, smoother curves for detailed analysis
Higher density provides better accuracy but may take longer to render for complex functions.
How do I save or share my graphs?
Use the "Save" button to save your current graph configuration to your browser's local storage. The "Share" button allows you to generate a shareable link that you can send to others. When they open the link, they'll see the same functions and settings you used.
What types of functions are supported?
The grapher supports a wide range of functions including:
  • Polynomials (e.g., x^3 - 2x + 1)
  • Trigonometric functions (sin, cos, tan)
  • Exponential and logarithmic functions
  • Rational functions
  • Absolute value functions
  • Square roots and other radicals
For a complete list, see the "Function Types" section in the sidebar.