Domain and Range Calculator
Find the exact domain and range of any function step-by-step in interval notation.
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Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.
How to Find Domain and Range
To find the domain, identify values of x where the function is undefined—such as division by zero, square roots of negative numbers, or non-positive logarithm arguments. To find the range, analyze the function's minimum and maximum values, horizontal asymptotes, or invertibility.
Frequently Asked Questions
What is the domain of a function?
The domain is the set of all possible input values (x-values) for which the function is defined and produces a real number output.
What is the range of a function?
The range is the complete set of all resulting output values (y-values) that the function can produce across its entire domain.
How do you write domain and range in interval notation?
Interval notation uses brackets [ ] for included endpoints and parentheses ( ) for excluded values and infinity. For example, [0, ∞) means all numbers greater than or equal to 0.
What causes values to be excluded from the domain?
The two most common restrictions in real-valued functions are division by zero (denominators cannot equal zero) and negative values inside even roots (radicands must be ≥ 0).
What are the domain and range of 1/x and √x?
For f(x) = 1/x, the domain and range are both (-∞, 0) ∪ (0, ∞). For f(x) = √x, the domain and range are both [0, ∞).