Advanced Graphing Calculator
Graph mathematical functions, compute derivatives and integrals, find critical points, and explore parametric and polar equations with an interactive visual display. Supports multiple functions, calculus analysis, and advanced coordinate systems.
Function Graph
Functions
Analysis
Enter a function to see analysis results.
Supported Functions
Arithmetic
+, -, *, /, ^
Trigonometric
sin, cos, tan, asin, acos, atan
Exponential
exp, log, log10, sqrt, abs
Constants
pi, e
How to Use This Calculator
- Enter one or more mathematical expressions to plot them on the graph. You can visualize functions, compare curves, and explore how changing parameters shifts the shape.
- Graphing Mode — Select the type of graphing you want to perform. Choose from: Standard Graphing (up to 4 functions), Calculus Analysis (derivatives, integrals), Parametric Equations, Polar Coordinates, Limits. default: 0.
- f₁(x) — Enter a function of x. Examples: x^2, sin(x), log(x), exp(-x^2)
- f₂(x) — Optional second function
- f(x) — Enter the function to analyze. Supports: +, -, *, /, ^, sin, cos, tan, log, exp, sqrt, abs
- Show Derivative on Graph — enter your preferred option from the dropdown. Choose from: Yes, No. default: 1.
- x(t) — Enter x as a function of t
- y(t) — Enter y as a function of t
- t min — Start value for parameter t default: 0.
- t max — End value for parameter t (2π ≈ 6.283) default: 6.283.
- r(θ) — Enter r as a function of theta. Use 'theta' for the angle variable.
- θ min — Start angle in radians default: 0.
- θ max — End angle in radians (2π ≈ 6.283) default: 6.283.
- f(x) — Enter the function to find the limit of
- x approaches — The value x approaches default: 0.
- Expand "Advanced Options" for additional fine-tuning. These optional inputs let you model more specific scenarios:
- f₃(x) — Optional third function
- f₄(x) — Optional fourth function
- X Min — Left boundary of the graph default: -10.
- X Max — Right boundary of the graph default: 10.
- Resolution — Higher resolution = smoother curves but slower rendering Choose from: Low (100 points), Medium (200 points), High (500 points), Ultra (1000 points). default: 200.
- Once all inputs are set, review your results in the Results panel. Here's what each output means:
- First Derivative f'(x) — your calculated result. This is the primary result of this calculator.
- Limit — your calculated result. This is the primary result of this calculator.
- Second Derivative f''(x) — your calculated result.
- Definite Integral — your calculated result.
- Integration Bounds — your calculated result.
- X-Intercepts (Roots) — your calculated result.
- Local Minima — your calculated result.
- Local Maxima — your calculated result.
- Left-Hand Limit — your calculated result.
- Right-Hand Limit — your calculated result.
- Limit Exists — your calculated result.
- Parameter Range — your calculated result.
- Angle Range — your calculated result.
- dx/dt — your calculated result.
- dy/dt — your calculated result.
- dr/dθ — your calculated result.
- Error — your calculated result.
- Explore the related calculators below if you need deeper analysis or want to approach this topic from a different angle.
Related Calculators
Quadratic Equation Solver
Solve quadratic equations (ax² + bx + c = 0). Find roots, discriminant, vertex, and axis of symmetry with a visual graph.
Scientific Calculator
Scientific calculator with multiple modes and expression input
Linear Regression Calculator
Calculate linear regression line, slope, intercept, and R-squared. Find the best-fit line for your data points.
Logarithm Calculator
Calculate logarithms with any base. Get log base 10, natural log (ln), log base 2, and custom base logarithms instantly.
Standard Deviation Calculator
Calculate the mean, median, standard deviation, and variance for a set of numbers. Supports both population and sample calculations.