Taxonomy Distribution Report

Overview

• Total Concepts: 208
• Number of Taxonomies: 13
• Average Concepts per Taxonomy: 16.0

Distribution Summary

Category	TaxonomyID	Count	Percentage	Status
Foundation Concepts	FOUND	27	13.0%	✅
Algebra Foundations	ALG	23	11.1%	✅
Graphing and Visualization	GRAPH	22	10.6%	✅
Quadratic Functions	QUAD	21	10.1%	✅
Linear Functions	LIN	18	8.7%	✅
Polynomial Functions	POLY	16	7.7%	✅
Function Classifications	CLASS	15	7.2%	✅
Inverse and Composite	INVC	13	6.2%	✅
Transformations	TRANS	13	6.2%	✅
Rational Functions	RAT	11	5.3%	✅
Exponential Functions	EXP	11	5.3%	✅
Logarithmic Functions	LOG	9	4.3%	✅
Modeling and Applications	MODEL	9	4.3%	✅

Visual Distribution

Foundation Concepts       ██████  27 ( 13.0%)
Algebra Foundations       █████  23 ( 11.1%)
Graphing and Visualizatio █████  22 ( 10.6%)
Quadratic Functions       █████  21 ( 10.1%)
Linear Functions          ████  18 (  8.7%)
Polynomial Functions      ███  16 (  7.7%)
Function Classifications  ███  15 (  7.2%)
Inverse and Composite     ███  13 (  6.2%)
Transformations           ███  13 (  6.2%)
Rational Functions        ██  11 (  5.3%)
Exponential Functions     ██  11 (  5.3%)
Logarithmic Functions     ██   9 (  4.3%)
Modeling and Applications ██   9 (  4.3%)

Balance Analysis

✅ No Over-Represented Categories

All categories are under the 30% threshold. Good balance!

Category Details

Foundation Concepts (FOUND)

Count: 27 concepts (13.0%)

Concepts:

• 1. Relation
• 1. Function
• 1. Domain
• 1. Range
• 1. Input Variable
• 1. Output Variable
• 1. Function Notation
• 1. Dependent Variable
• 1. Independent Variable
• 1. Mapping Diagram
• 1. Vertical Line Test
• 1. Ordered Pair
• 1. Coordinate Plane
• 1. X-Axis
• 1. Y-Axis
• ...and 12 more

Algebra Foundations (ALG)

Count: 23 concepts (11.1%)

Concepts:

• 1. Real Number Line
• 1. Parameter
• 1. Coefficient
• 1. Variable
• 1. Constant
• 1. Expression
• 1. Equation
• 1. Inequality
• 1. Solution Set
• 1. Number Systems
• 1. Integers
• 1. Rational Numbers
• 1. Irrational Numbers
• 1. Real Numbers
• 1. Substitution Method
• ...and 8 more

Graphing and Visualization (GRAPH)

Count: 22 concepts (10.6%)

Concepts:

• 1. Graph of a Function
• 1. Y-Intercept
• 1. X-Intercept
• 1. Graphing Technology
• 1. Window Settings
• 1. Sketching vs Drawing
• 1. Key Graph Features
• 1. Turning Points
• 1. Maximum Point
• 1. Minimum Point
• 1. Roots of a Function
• 1. Zeros of a Function
• 1. Function Intercepts
• 1. Intersection of Curves
• 1. Increasing Function
• ...and 7 more

Quadratic Functions (QUAD)

Count: 21 concepts (10.1%)

Concepts:

• 1. Axis of Symmetry
• 1. Quadratic Function
• 1. Parabola
• 1. Standard Form Quadratic
• 1. Factored Form Quadratic
• 1. Vertex Form Quadratic
• 1. Vertex of a Parabola
• 1. Completing the Square
• 1. Quadratic Formula
• 1. Factoring Quadratics
• 1. Discriminant
• 1. Two Real Roots
• 1. Equal Real Roots
• 1. No Real Roots
• 1. Nature of Roots
• ...and 6 more

Linear Functions (LIN)

Count: 18 concepts (8.7%)

Concepts:

• 1. Linear Function
• 1. Slope
• 1. Gradient-Intercept Form
• 1. General Form of a Line
• 1. Point-Gradient Form
• 1. Gradient Calculation
• 1. Positive Gradient
• 1. Negative Gradient
• 1. Zero Gradient
• 1. Undefined Gradient
• 1. Parallel Lines
• 1. Perpendicular Lines
• 1. Linear Equation Solving
• 1. Simultaneous Equations
• 1. Intersection of Lines
• ...and 3 more

Polynomial Functions (POLY)

Count: 16 concepts (7.7%)

Concepts:

• 1. Polynomial Function
• 1. Degree of a Polynomial
• 1. Leading Coefficient
• 1. Cubic Function
• 1. Quartic Function
• 1. End Behavior
• 1. Turning Points Count
• 1. Factor Theorem
• 1. Remainder Theorem
• 1. Polynomial Division
• 1. Synthetic Division
• 1. Root Finding
• 1. Sum of Roots Formula
• 1. Product of Roots Formula
• 1. Multiplicity of Roots
• ...and 1 more

Function Classifications (CLASS)

Count: 15 concepts (7.2%)

Concepts:

• 1. Even Function
• 1. Odd Function
• 1. Symmetry Testing
• 1. Periodic Function
• 1. Modulus Function
• 1. Graph of Modulus
• 1. Absolute Value Equations
• 1. Y Equals Mod F of X
• 1. Y Equals F of Mod X
• 1. Y Equals F of X Squared
• 1. Piecewise Function
• 1. Step Function
• 1. Signum Function
• 1. Greatest Integer Function
• 1. Function Behavior Analysis

Inverse and Composite (INVC)

Count: 13 concepts (6.2%)

Concepts:

• 1. Inverse Function
• 1. Inverse Function Notation
• 1. Finding an Inverse
• 1. Reflection Over Y Equals X
• 1. One-to-One Function
• 1. Horizontal Line Test
• 1. Self-Inverse Function
• 1. Composite Function
• 1. Function Composition Rule
• 1. Order of Composition
• 1. Domain of Composite
• 1. Decomposing Functions
• 1. Domain Restriction Inverse

Transformations (TRANS)

Count: 13 concepts (6.2%)

Concepts:

• 1. Translation
• 1. Horizontal Translation
• 1. Vertical Translation
• 1. Reflection in X-Axis
• 1. Reflection in Y-Axis
• 1. Vertical Stretch
• 1. Horizontal Stretch
• 1. Scale Factor
• 1. Composite Transformation
• 1. Transformation Notation
• 1. Effect on Coordinates
• 1. Transformation of Points
• 1. Graph Transformation Order

Rational Functions (RAT)

Count: 11 concepts (5.3%)

Concepts:

• 1. Reciprocal Function
• 1. Hyperbola
• 1. Vertical Asymptote
• 1. Horizontal Asymptote
• 1. Asymptotic Behavior
• 1. Rational Function
• 1. Rational Form Ax Plus B
• 1. Oblique Asymptote
• 1. Graphing Rational Functions
• 1. Holes in Rational Graphs
• 1. Domain Restrictions

Exponential Functions (EXP)

Count: 11 concepts (5.3%)

Concepts:

• 1. Exponential Function
• 1. Base of an Exponential
• 1. Exponential Growth
• 1. Exponential Decay
• 1. Natural Exponential
• 1. Euler's Number
• 1. Exponential Equations
• 1. Compound Interest Model
• 1. Population Growth Model
• 1. Half-Life Model
• 1. Graphing Exponentials

Logarithmic Functions (LOG)

Count: 9 concepts (4.3%)

Concepts:

• 1. Logarithmic Function
• 1. Common Logarithm
• 1. Natural Logarithm
• 1. Logarithm Laws
• 1. Change of Base Rule
• 1. Solving Log Equations
• 1. Log-Exponential Inverse
• 1. Logarithmic Scale
• 1. Graphing Logarithms

Modeling and Applications (MODEL)

Count: 9 concepts (4.3%)

Concepts:

• 1. Function Modeling
• 1. Regression Model
• 1. Curve Fitting
• 1. Extrapolation
• 1. Interpolation
• 1. Mathematical Modeling Cycle
• 1. Units and Dimensions
• 1. Significant Figures
• 1. Exact vs Approximate

Recommendations

• ✅ Excellent balance: Categories are evenly distributed (spread: 8.7%)
• ✅ MISC category minimal: Good categorization specificity

Educational Use Recommendations

• Use taxonomy categories for color-coding in graph visualizations
• Design curriculum modules based on taxonomy groupings
• Create filtered views for focused learning paths
• Use categories for assessment organization
• Enable navigation by topic area in interactive tools

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Report generated by learning-graph-reports/taxonomy_distribution.py