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Domain and Range Calculator

Enter the function, then click “Calculate” to instantly get the domain, range, and graph of the function.

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Domain and Range Calculator

This domain and range calculator helps you find all possible input (domain) and output (range) values for any function. Results are shown in interval notation and include a graph to visualize where the function is defined and what values it can produce.

What Are Domain and Range?

The domain and range describe all valid inputs and outputs of a function, giving insight into its behavior.

Domain:

The set of all possible input values (x-values) for a function. It defines the values of x for which the function is valid. Learn more about functions.

Range:

The set of all possible output values (y-values) that the function produces when evaluated over its domain.

Domain and Range of Function

Notation:

Interval notation: (-∞, +∞), [0, +∞)
Set-builder notation: {x ∣ x > 0}
Inequality notation: x > 0, y ≤ 5

How to Use the Calculator

Step 1: Enter the Function

Input your function f(x) in the calculator field.

Step 2: Click "Calculate"

The calculator processes the function and provides the domain and range.

Step 3: Review Results

Domain and range values in interval notation
Graphical view showing where the function exists

Input Rules:

Use lowercase letters only
Always use x as the variable

Supported Functions:

Polynomial: x^2 + 3x + 2
Rational: 1 / (x - 4)
Root: sqrt(x), cbrt(x)
Exponential & Logarithmic: e^x, log(x)

Limitations & Syntax Tips:

Complex numbers are not supported
Use parentheses accurately
Exponents: x^3
Multiplication: 2*x instead of 2x
Constants: pi, e

Why Use a Domain and Range Calculator?

Instant Calculation: Quickly get results without manual errors
Graphical Visualization: See the domain and range on a graph
Supports Various Functions: Polynomial, rational, root, exponential, logarithmic
Handles Restrictions Automatically: Division by zero, negative roots, undefined values

Example: Finding Domain and Range

Function:

y = (x + 3) / (10 - x)

Solution:

Domain:

Denominator cannot be zero: 10 - x ≠ 0 → x ≠ 10

✅ Domain: x ∈ (-∞, 10) ∪ (10, ∞)

Range:

y = (x + 3) / (10 - x)

Solving for x: y(10 - x) = x + 3 → x = (10y - 3)/(-y - 1)

Denominator cannot be zero: -y - 1 ≠ 0 → y ≠ -1

✅ Range: y ∈ (-∞, -1) ∪ (-1, ∞)

Interpreting Results:

Domain:

The domain shows all valid x-values. Example: x ∈ (-∞, 10) ∪ (10, ∞) excludes x = 10.

Range:

The range shows all possible outputs. Example: y ∈ (-∞, -1) ∪ (-1, ∞) excludes y = -1.

Continuity, Restrictions & Asymptotes:

Continuity: No gaps, holes, or breaks in the graph
Restrictions: Values causing division by zero or negative roots
Vertical Asymptotes: Function approaches ±∞ at restricted x-values (e.g., x = 10)
Horizontal Asymptotes: Function approaches a line as x → ±∞ (e.g., y = 1)
Holes: Points where numerator and denominator are zero, creating gaps

Common Mistakes:

Forgetting when the denominator equals zero
Negative values inside a square root for real functions
Misinterpreting interval endpoints (use parentheses for excluded, brackets for included)
Ignoring complex or imaginary domains