Math & Algebra Tool

Function Grapher

Plot mathematical functions.

510-55
X: [-10, 10], Y: [-10, 10]

Σ The Formula

Plot y = f(x) for any function | Supports: x^n, sin(x), cos(x), tan(x), log(x), exp(x)

Real World Examples

Parabola
y = x^2 creates a U-shaped curve
Sine Wave
y = sin(x) creates periodic oscillation
Exponential
y = exp(x) shows rapid growth
Rational
y = 1/x shows hyperbola with asymptotes

# About This Calculator

Function graphing is the visual representation of mathematical relationships, showing how output (y) changes as input (x) varies. Graphs reveal patterns, trends, intercepts, maxima/minima, and behavior that aren't obvious from equations alone. Visualization is key to understanding mathematics.

Graphing is essential in calculus (finding derivatives, integrals), physics (motion graphs, wave functions), economics (supply/demand curves), engineering (signal processing), and data science (trend analysis). Being able to visualize functions helps build mathematical intuition and solve complex problems.

This grapher supports common functions: polynomials (x^2, x^3), trigonometric (sin, cos, tan), exponential (exp), logarithmic (log), and combinations. Use standard notation: x^2 for x², sqrt(x) for √x, sin(x) for sine. The graph updates in real-time as you type.

Perfect for exploring function behavior, verifying homework, understanding transformations (shifts, stretches), finding roots/intercepts, or analyzing any mathematical relationship. Adjust the viewing window to zoom in on interesting features or see the big picture.

How To Use

  1. Enter function (e.g. x^2, sin(x), x+2).
  2. Click Plot.

Frequently Asked Questions

What functions can I graph?+

Polynomials (x^2, x^3), trig (sin(x), cos(x), tan(x)), exponential (exp(x)), logarithmic (log(x)), square root (sqrt(x)), absolute value (abs(x)), and combinations like sin(x^2) or x*exp(-x). Use standard math notation.

How do I graph multiple functions at once?+

This calculator graphs one function at a time. To compare functions, graph each separately or use graphing software like Desmos or GeoGebra. You can screenshot individual graphs and compare them side-by-side.

What do intercepts tell me?+

X-intercepts (where graph crosses x-axis, y=0) are the roots/zeros of the function - solutions to f(x)=0. Y-intercept (where graph crosses y-axis, x=0) is f(0). These points are crucial for understanding function behavior and solving equations.

Why does my graph have gaps or vertical lines?+

Gaps occur at undefined points (like 1/x at x=0, or log(x) at x≤0). Vertical lines suggest asymptotes - values where the function approaches infinity. This is normal behavior for rational and logarithmic functions.

How do I find maximum or minimum points?+

Visually locate peaks (maxima) and valleys (minima) on the graph. For precise values, use calculus (set derivative = 0) or numerical methods. The graph helps you estimate where these critical points occur.

Is Function Grapher free to use?+

Yes, Function Grapher on Matheric is completely free to use. We believe in accessible education and utility for everyone.

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