Domain & Range Explorer Pro

Function / Relation Type Polynomial

Notation Style

Parameters

Restrict Domain Bounds

Domain Min (x_min): -3.0

Min Endpoint:

Domain Max (x_max): 3.0

Max Endpoint:

Display Controls

1:1 Square Aspect Show Grid Projection Lines Show Asymptotes Point Inspector

Visual Color Key

Overall Curve

Restricted Curve

Domain / VA

Range / HA

Interactive Canvas Viewport

Hover canvas to inspect (x, y)

Equation / Relation

Asymptotes

Domain (X)

Range (Y)

Disjoint Range Detected: The interval splits across an asymptote or discontinuous boundary, resulting in separate intervals rendered vertically above.

Piecewise Function Builder

Define custom function rules across sub-intervals to visualize piecewise domain and range combination.

Piecewise Sub-Intervals

Piecewise Total Domain

Piecewise Total Range

Interactive Practice Quiz

Test your mastery of finding domain, range, and asymptotes for various mathematical relations.

Score

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Polynomial Function Question #1

Determine the Domain of the following relation:

Domain & Range Comprehensive Reference

Quick mathematical rules, interval notation guides, and asymptote cheat sheet.

The 3 Key Algebraic Domain Restrictions

1. Denominators Cannot Be Zero

For rational functions f(x) = a/(x - h) + k, set x - h ≠ 0 to solve vertical asymptote at x = h.

2. Even Radicands Must Be Non-Negative

For square roots f(x) = √(g(x)), the expression inside must satisfy g(x) ≥ 0.

3. Logarithm Arguments Must Be Strictly Positive

For logarithmic functions f(x) = ln(g(x)), the argument must satisfy g(x) > 0.

Inequality & Interval Notation Guide

a ≤ x ≤ b ⇔ [a, b] Closed interval (includes both a and b)

a < x < b ⇔ (a, b) Open interval (excludes endpoints)

a ≤ x < b ⇔ [a, b) Half-open (includes a, excludes b)

x ≠ h ⇔ (-∞, h) ∪ (h, ∞) All real numbers except asymptote h

x ≥ c ⇔ [c, ∞) Half-bounded ray extending to infinity