Domain & Range Explorer Pro

Function / Relation Type Polynomial

Parameters

Restrict Domain Bounds

Domain Min (x_min): -3.0

Domain Max (x_max): 3.0

Display Controls

1:1 Square Aspect Show Grid Projection Lines Point Inspector

Visual Color Key

Overall Curve

Restricted Curve

Domain (X-Axis)

Range (Y-Axis)

Interactive Canvas Viewport

Hover canvas to inspect (x, y)

Equation / Relation

Domain (X)

Range (Y)

Disjoint Range Detected: The domain restriction splits this non-function relation curve into disjoint upper and lower arcs, resulting in two distinct range intervals joined by the union symbol \cup.

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 and range for various mathematical relations.

Score

0 / 0

Streak

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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 algebraic restriction cheat sheet.

The 3 Key Algebraic Domain Restrictions

1. Denominators Cannot Be Zero

For rational functions f(x) = g(x)/h(x), set h(x) ≠ 0 to solve domain holes or vertical asymptotes.

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.

Interval & Set Notation Guide

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

(a, b) Open interval (excludes endpoints)

[a, b) Half-open (includes a, excludes b)

(-∞, ∞) All real numbers (ℝ)

A ∪ B Union of disjoint sets (combines separate intervals)