What types of functions can I graph?

You can graph polynomial functions, trigonometric functions, exponential functions, logarithmic functions, rational functions, and more. Examples: x^2, sin(x), e^x, ln(x), 1/x.

How do I find roots and intersections?

Use the analysis tools to find roots (where function crosses x-axis), extrema (maximum/minimum points), and intersections between multiple functions.

Can I plot multiple functions simultaneously?

Yes, you can plot up to 5 functions simultaneously in different colors for easy comparison and analysis.

What syntax should I use when entering functions?

Use standard mathematical notation: + - * / for basic operations, ^ for exponents, sin(x), cos(x), ln(x), sqrt(x), abs(x) for functions. Use parentheses for grouping.

Can I save or export my graphs?

Yes, click the Export button to save your graph as an image file for use in homework, presentations, or reports.

How do I navigate and zoom the graph?

Click and drag to pan, use scroll wheel to zoom, or use the control buttons. You can also manually set viewing window values.

Graph Calculator

Functions

f₁(x) =

f₂(x) =

f₃(x) =

f₄(x) =

f₅(x) =

x: 0, y: 0

X Min

X Max

Y Min

Y Max

X Scale

Y Scale

Function Analysis

What is a Graph Calculator?
This advanced graphing tool allows you to plot mathematical functions, analyze their properties, and explore mathematical relationships visually. Perfect for calculus, algebra, and advanced mathematics.

Current Analysis

Status

Ready to graph functions

Function Examples

Related Math Calculators

How to Use the Graph Calculator

Enter Functions: Type mathematical expressions using x as the variable in the function input fields.
Function Syntax: Use ^ for powers, * for multiplication, sin(), cos(), tan(), ln(), sqrt(), abs(), and more.
Toggle Functions: Click ON/OFF buttons to show/hide individual functions on the graph.
Navigate the Graph: Click and drag to pan around, use mouse wheel to zoom in/out.
Trace Mode: Enable trace mode to follow function curves and see exact coordinates.
Analysis Tools: Use the analysis buttons to find roots, extrema, intersections, and other function properties.
Customize View: Adjust the window settings (X/Y min/max) and scale to focus on specific regions.
Export: Save your graphs as images for reports or presentations.

Supported Functions

Basic Functions

Polynomial: x^2, x^3 + 2*x - 1, x^4 - 5*x^2 + 4
Linear: 2*x + 3, -0.5*x + 7
Rational: 1/x, (x^2-1)/(x+1), (x+2)/(x^2-4)
Radical: sqrt(x), x^(1/3), sqrt(x^2-4)
Absolute Value: abs(x), abs(x-2), abs(x^2-4)

Advanced Functions

Trigonometric: sin(x), cos(x), tan(x), sec(x), csc(x), cot(x)
Inverse Trig: asin(x), acos(x), atan(x)
Exponential: e^x, 2^x, 10^x, a^x
Logarithmic: ln(x), log(x), log2(x)
Hyperbolic: sinh(x), cosh(x), tanh(x)
Combined: sin(x^2), e^(-x^2), ln(abs(x))

Features

Plot up to 5 functions simultaneously in different colors
Interactive zoom, pan, and trace capabilities
Function analysis tools (roots, extrema, intersections)
Customizable viewing window and grid scaling
Real-time coordinate display while moving mouse

Export functionality to save graphs as images
Responsive design that works on all devices
Support for complex mathematical expressions
Grid display with adjustable scaling
Professional-quality graphs suitable for education

Real-Life Examples

Physics & Engineering

Projectile Motion: Plot y = -16*x^2 + 32*x + 6 to model the height of a ball over time
Wave Functions: Use sin(x) and cos(x) to analyze sound waves and vibrations
Exponential Decay: Model radioactive decay with y = 100*e^(-0.1*x)
Population Growth: Use y = 1000*e^(0.05*x) to predict population changes
Cooling/Heating: Newton's law of cooling: T = 20 + 50*e^(-0.1*x)

Business & Economics

Revenue Analysis: Plot R = -2*x^2 + 20*x to find optimal pricing
Cost Functions: Model production costs with C = 50 + 3*x + 0.01*x^2
Supply & Demand: Compare linear functions to find market equilibrium
Investment Growth: Compound interest: A = 1000*(1.08)^x
Break-even Analysis: Find where revenue equals cost functions

Biology & Medicine

Drug Concentration: Model blood drug levels with C = 10*e^(-0.2*x)
Bacterial Growth: Use N = 100*2^x to track colony expansion
Heart Rate Zones: Plot target heart rates across age ranges
Enzyme Activity: Michaelis-Menten kinetics: v = (V*x)/(K+x)

Environmental Science

Temperature Cycles: Model seasonal changes with T = 15 + 10*sin(x/6)
Carbon Emissions: Track pollution levels over time
Species Population: Logistic growth: P = K/(1+e^(-r*x))
Water Flow: Model river discharge rates throughout the year

Frequently Asked Questions

You can graph a wide variety of functions including:

Polynomial functions: x^2, x^3 + 2*x - 1, x^4 - 5*x^2 + 4
Trigonometric functions: sin(x), cos(x), tan(x), and their inverses
Exponential and logarithmic: e^x, 2^x, ln(x), log(x)
Rational functions: 1/x, (x^2-1)/(x+1)
Radical functions: sqrt(x), x^(1/3)
Absolute value: abs(x), abs(x-2)
Composite functions: sin(x^2), e^(-x^2), ln(abs(x))

Use the Function Analysis tools:

Find Roots: Calculates where the function crosses the x-axis (f(x) = 0)
Find Extrema: Locates maximum and minimum points of the function
Intersections: Finds where two or more functions cross each other
Area Under Curve: Calculates the definite integral between specified bounds
Derivative: Shows the derivative function to analyze rates of change

Simply click the appropriate analysis button after plotting your functions.

Yes! You can plot up to 5 functions simultaneously. Each function has:

Its own color-coded input field (blue, green, red, yellow, cyan)
An ON/OFF toggle button to show or hide the function
Individual analysis capabilities

This is perfect for comparing functions, finding intersections, or studying function families.

Use standard mathematical notation with these operators:

Basic operations: + (add), - (subtract), * (multiply), / (divide)
Exponents: ^ (e.g., x^2 for x squared)
Functions: sin(x), cos(x), tan(x), ln(x), log(x), sqrt(x), abs(x)
Constants: Use 'e' for Euler's number, 'pi' for π
Parentheses: Use () to group operations

Examples: x^2 + 3*x - 2, sin(2*x), e^(-x^2), sqrt(x+1)

Multiple ways to navigate:

Mouse Controls: Click and drag to pan, use scroll wheel to zoom
Control Buttons: Use Zoom In, Zoom Out, and Reset View buttons
Window Settings: Manually set X/Y min/max values and scale
Trace Mode: Enable to follow function curves and see exact coordinates

The coordinate display in the top-right shows your current mouse position.

Yes! Click the "Export" button to save your graph as an image file. This is useful for:

Including graphs in homework assignments or reports
Creating presentations or study materials
Sharing mathematical concepts with others
Documentation for research or analysis

The exported image includes all visible functions, grid lines, and labels.

Absolutely! This calculator is designed for educational purposes and is suitable for:

High School: Algebra, Pre-Calculus, Trigonometry courses
College: Calculus, Statistics, Physics, Engineering courses
Professional: Data analysis, research, and technical presentations
Self-Study: Exploring mathematical concepts and relationships

However, always check your institution's calculator policy for exams and assignments.

Common troubleshooting steps:

Check syntax: Ensure proper use of operators and parentheses
Verify the toggle: Make sure the function is set to "ON"
Adjust window: The function might be outside the current viewing area
Check domain: Some functions have restricted domains (e.g., ln(x) only works for x > 0)
Use explicit multiplication: Write 2*x instead of 2x

Try the function examples if you're unsure about syntax.