Graphing Calculator

How to Use This Graphing Calculator

Enter mathematical expressions in the Expressions panel on the left using standard math notation. Each expression is assigned a unique color and plotted in real-time. You can add multiple functions, toggle their visibility, or remove them individually. Navigate the graph by dragging (click and drag), zooming with the scroll wheel, and pinch-to-zoom on mobile.

Expression Syntax Guide

This calculator uses math.js expression syntax. All variables are in terms of x. Key syntax rules:

• Multiplication requires *: Write 2*x not 2x. Write x*sin(x) not xsin(x).
• Exponents use ^: x^2 = x squared, x^3 = x cubed, 2^x = exponential growth
• Built-in functions: sin(x), cos(x), tan(x), sqrt(x), abs(x), log(x), exp(x)
• Constants: Use pi for π and e for Euler's number
• Division: Use / for division. Example: 1/x plots a hyperbola

Example expressions to try: x^2 - 4, sin(x), sin(x)/x, x^3 - 3*x, 2*x + 1, abs(x), exp(-x^2)

Reading a Graph: Key Concepts

• X-intercepts (roots/zeros): Where the function line crosses the x-axis (y = 0). These are the solutions to the equation f(x) = 0.
• Y-intercept: Where the line crosses the y-axis (x = 0). Shows the function's value when x = 0.
• Slope: For linear functions (y = mx + b), the slope m shows how steeply the line rises/falls. Positive = going up, negative = going down.
• Local maximum/minimum: The highest or lowest points of a curve in a given region. Useful for optimization problems.
• Asymptotes: Lines the function approaches but never touches. Common in functions like 1/x (vertical asymptote at x=0, horizontal asymptote at y=0).

Real-World Applications of Graphing

• Physics: Model projectile motion (parabolic quadratic), oscillation (sine waves), and exponential decay (radioactive half-life)
• Economics: Visualize supply/demand curves, cost functions, and break-even points where two functions intersect
• Engineering: Analyze signal waveforms, control system responses, and structural load distributions
• Statistics: Plot normal distribution curves (bell curves), probability density functions, and regression lines