Loading the page...
Preparing tools and content for you. This usually takes a second.
Preparing tools and content for you. This usually takes a second.
Fetching calculator categories and tools for this section.
Free domain and range calculator & domain range graph calculator. Find domain and range of functions with interval notation, analyze restrictions, and understand function behavior. Our calculator helps you determine valid inputs and outputs for polynomial, rational, radical, logarithmic, exponential, and trigonometric functions.
Last updated: February 2, 2026
Need a custom function analysis calculator for your platform? Get a Quote
Enter polynomials like x², x³, or x⁴
Domain:
All real numbers
(-∞, +∞)
Range:
All real numbers ≥ minimum value
[yₘᵢₙ, +∞)
Restrictions:
No restrictions
Analysis:
Quadratic function with positive leading coefficient: parabola opens upward
Key Concepts:
Function types
All major types
Analyzes polynomial, rational, radical, logarithmic, exponential, and trig functions
Visual analysis
Graph interpretation
Understand domain and range by analyzing function graphs and behavior
Analysis method
Algebraic & graphical
Uses multiple methods to determine complete domain and range
Focus on input
Valid x-values
Identifies restrictions like division by zero, negative radicals
Focus on output
Valid y-values
Determines all possible output values based on function behavior
Notation format
[a, b], (a, b), ∪
Converts domain and range to standard interval notation format
For function f(x) = x² (quadratic):
Domain
(-∞, +∞)
All real numbers
Range
[0, +∞)
y ≥ 0
Our domain and range calculator analyzes mathematical functions using algebraic principles to determine valid input values (domain) and output values (range). The calculation identifies restrictions like division by zero, negative numbers under square roots, and logarithms of non-positive values.
Each function type has characteristic domain and range patterns based on its mathematical properties. Understanding these patterns helps quickly identify valid inputs and outputs.
Shows valid x and y values for different function types
Finding domain and range requires understanding function behavior and restrictions. The domain consists of all x-values for which the function produces a real number output. The range consists of all y-values that the function can actually produce. Interval notation provides a concise way to express these sets.
Need help with other function tools? Check out our vertex calculator and intercept calculator.
Get Custom Calculator for Your PlatformResult: Domain: (-∞, 2) ∪ (2, +∞), Range: (-∞, 0) ∪ (0, +∞)
Vertical asymptote at x = 2, horizontal asymptote at y = 0
f(x) = √(x - 3)
Domain: [3, +∞), Range: [0, +∞)
f(x) = ln(x + 1)
Domain: (-1, +∞), Range: (-∞, +∞)
Share it with others who need help with function analysis
Suggested hashtags: #Mathematics #DomainRange #Functions #Algebra #Calculator