2D Function Graph Generator
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Understanding Function Graphs
What are Function Graphs?
A function graph is a visual representation of a mathematical function in a coordinate system.
Key Concepts:
- Domain and Range
- Continuity
- Derivatives
- Critical Points
- Asymptotes
- Periodicity
Types of Functions
- Polynomial Functions
- Linear: f(x) = ax + b
- Quadratic: f(x) = ax² + bx + c
- Cubic: f(x) = ax³ + bx² + cx + d
- Transcendental Functions
- Trigonometric: sin(x), cos(x), tan(x)
- Exponential: e^x, a^x
- Logarithmic: ln(x), log₁₀(x)
- Special Functions
- Rational Functions
- Piecewise Functions
- Inverse Functions
Graph Analysis
Behavior
Limits and Continuity
Shape
Concavity and Inflection
Features
Zeros and Extrema
Symmetry
Even and Odd Functions
Advanced Topics
- Calculus Applications
- Rate of Change
- Area Under Curve
- Optimization
- Complex Analysis
- Complex Roots
- Singularities
- Branch Points