Mathswell MATHSWELL

📈 Function Analyzer

Build, test, and analyze mathematical functions interactively

What Makes a Function?

A function is a special relationship where each input (x-value) has exactly one output (y-value). The vertical line test helps us check this!

📊 The Vertical Line Test

If any vertical line crosses a graph more than once, it's not a function.

Key Rule: One input → One output

🎯 Domain & Range

Domain: All possible x-values
Range: All possible y-values

Example: f(x) = x²
Domain: (-∞, ∞)
Range: [0, ∞)

📈 Function Behavior

• Increasing: Going up ↗
• Decreasing: Going down ↘
• Constant: Staying flat →
• Concave Up: Holds water ∪
• Concave Down: Sheds water ∩

Interactive Demo: Test Different Graphs!

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🛠️ Build Controls

📝 Segments

Type Domain Y-Values Curve Del

🔍 Live Analysis

Add segments to begin analysis.

🎯 Function Challenge

Challenge #1
Build a function with these properties:
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💡 AI feedback simulated locally for educational purposes. Results may vary. Always verify mathematical concepts with multiple sources.