Domain and Range Calculator: Interval Notation
This domain and range calculator finds where a function is defined and which output values it can reach. Enter a function of x such as sqrt(x − 3), 1/(x² − 4), ln(x) or (x + 1)/(x − 1) and it returns the domain and range in interval notation. For the domain, it finds the values that break the function: zero denominators, negative numbers under an even root, and logs of zero or negative numbers. For the range, it follows the function across each piece of the domain, finding minimums, maximums and the values it approaches near asymptotes and at the far ends.
Domain and Range Calculator
Find the domain and range of a function in interval notation, including gaps from division by zero, roots and logs.
How to use the Domain and Range Calculator
- Type your function using x.
- Read the domain in interval notation.
- Read the range in interval notation.
- Use the notes to see what limits the domain.
How the domain and range are found
Domain: all real x except zeros of denominators, x making even-root arguments negative, and x making log arguments ≤ 0. Range: the union, over each domain piece, of values between the lowest and highest outputs, including limits near breaks and as x → ±∞.
Features
- Interval notation with ∪ for gaps
- Fractions, even roots and logs
- Polynomials, exponentials, abs, sin and cos
- Asymptote and end behavior
- Exact values like −1/4 and ฯ/2
Frequently asked questions
What is the domain of a function?
The domain is the set of all x values you can put into the function and get a real number. For f(x) = √(x − 3), the domain is [3, ∞).
What is the range of a function?
The range is the set of all output values. For f(x) = x², the outputs are never negative, so the range is [0, ∞).
How do you find the domain of a fraction?
Set the denominator equal to zero and remove those x values. For 1/(x − 2), x cannot be 2, so the domain is (−∞, 2) ∪ (2, ∞).
What do brackets and parentheses mean in interval notation?
A square bracket [ ] means the endpoint is included, and a parenthesis ( ) means it is not. ∞ always gets a parenthesis.
What is the domain and range of a log function?
For ln(x), the domain is (0, ∞) because you cannot take the log of zero or a negative number, and the range is all real numbers, (−∞, ∞).