Domain and Range Calculator (Free, with Graph)

Use this free domain and range calculator to find the domain and range of common functions, linear, quadratic, square root, rational, exponential, and logarithmic, in interval notation, with a graph.

How to use it

1. Pick the function type.
2. Enter its parameters (for example a, h, k).
3. Press Find domain & range.

Quick rules

Square roots need a non-negative radicand; logs need a positive argument; rational functions exclude the value that makes the denominator zero. The graph helps you see the range.

Related: the Function Grapher and more free math calculators.

Domain and Range Rules for Each Function Family

Use this table to check the calculator’s answer or to work by hand. In each form, h shifts the graph sideways and k shifts it up or down.

Three worked examples to test yourself

1. f(x) = −2(x − 1)² + 5. Any x works, so the domain is (−∞, ∞). Since a = −2 is negative, the parabola opens down from its vertex (1, 5). Range: (−∞, 5].
2. f(x) = 1/(x + 4) − 1. The denominator is zero at x = −4, so the domain is all x except −4. The horizontal asymptote is y = −1, so the range is all y except −1.
3. f(x) = log(x − 2). The argument must be positive: x − 2 > 0, so x > 2. Domain: (2, ∞). A log can reach any output, so the range is (−∞, ∞).

Frequently asked questions

How do you write domain and range in interval notation?

Use square brackets for endpoints that are included, parentheses for endpoints that are not, and always use parentheses with ∞ or −∞. For f(x) = √(x + 5) − 1, the domain is [−5, ∞) because x + 5 cannot be negative, and the range is [−1, ∞) because the square root part is never below 0. Use ∪ to join separate pieces.

How do you find domain and range without a calculator?

Start with all real numbers and remove any x that causes a problem: a zero denominator, a negative number under an even root, or a log of zero or a negative number. For the range, think about which outputs are possible. For f(x) = 3/(x − 2), the domain is all x except 2, and the range is all y except 0, since 3 divided by a number is never 0.

How do you find domain and range on a TI-84 calculator?

A TI-84 does not list the domain and range directly, but the graph helps. Graph the function, use ZOOM and WINDOW to see its full shape, and TRACE to see where it starts or stops. For a parabola, use 2nd CALC minimum or maximum to find the vertex, which gives the boundary of the range. Then write the answer in interval notation yourself.

How do you find domain and range on Desmos?

Type the function and look at the graph from left to right for the domain and from bottom to top for the range. Click the curve to see key points such as a vertex or an endpoint with their coordinates. Watch for asymptotes, where the graph gets close to a line but never touches it, since those values are left out.

How do you find domain and range from a graph?

Read the domain along the x-axis, from the leftmost to the rightmost point of the graph, and the range along the y-axis, from the lowest to the highest point. A closed dot means the endpoint is included and an open dot means it is not. A line segment rising from a closed dot at (−3, 1) to an open dot at (4, 6) has domain [−3, 4) and range [1, 6).

How do you find the domain and range of a piecewise function?

Find the domain and range of each piece on its own interval, then combine them with a union. For f(x) = x + 1 when x < 0 and f(x) = 2 when x ≥ 0, the pieces cover every x, so the domain is (−∞, ∞). The first piece gives outputs in (−∞, 1) and the second gives only 2, so the range is (−∞, 1) ∪ {2}.

How to use the Domain and Range Calculator for homework

The Domain and Range Calculator is most useful when you treat it as a learning check, not just a shortcut to the final answer. Start by copying the original problem carefully, including signs, exponents, decimal points, fractions, parentheses, and units. Then enter the values in the same order the problem gives them. A small typing change can completely change the result, especially in algebra, statistics, geometry, and probability problems.

Before you press the button to calculate, make a quick estimate or prediction. The estimate does not need to be exact. Its job is to help you notice impossible answers. If a distance becomes negative, a probability is bigger than 1, an angle looks too large, or a decimal point seems misplaced, go back and check the input before trusting the final result.

Before you enter the problem

• Rewrite the problem in a clean line so every value is easy to see.
• Use parentheses around grouped expressions, especially in fractions and exponents.
• Keep units with the numbers while you work, even if the calculator only asks for the numbers.
• Check whether the problem wants an exact value, a decimal approximation, or a rounded answer.
• Look for restrictions such as positive values only, a chosen interval, or a required domain.

How to read the result

After the calculator gives a result, read more than the final line. If steps, tables, graphs, or intermediate values are shown, use them to understand how the answer was built. That is especially important when you are studying for a quiz or test, because teachers often give more credit for a correct process than for an unsupported number.

Try to identify the main idea behind the result. For example, ask yourself which formula was used, which operation changed the expression, which value controlled the graph, or which assumption made the answer possible. When you can explain that idea in your own words, the tool has helped you learn the skill instead of only checking one problem.

Common mistakes to avoid

Turn the answer into practice

One good way to study is to solve the problem by hand first, then use the Domain and Range Calculator to check your work. If your answer is wrong, do not erase everything immediately. Find the first line where your work stops matching the calculator's logic. That line is usually where the real misunderstanding happened.

1. Work the problem on paper and circle your final answer.
2. Use the calculator to check the result.
3. If the answers match, write one sentence explaining the method.
4. If they do not match, compare each step until you find the first difference.
5. Redo a similar problem without the tool to make sure the correction sticks.

When to use a calculator and when to work by hand

Use the Domain and Range Calculator when you want to check a long calculation, explore a pattern, test a graph, or confirm a result after practicing. Work by hand when the assignment asks for steps, when you are learning a new method, or when the test will not allow a digital tool. The strongest students use both: hand work to build understanding and calculators to check accuracy.

If you are preparing for a timed test, practice some problems without the tool and some with it. That balance helps you build speed while still understanding the math. Over time, the goal is to need the calculator less often for routine steps and use it more strategically for checking, exploring, and confirming your reasoning.

Quick accuracy checklist

Before you leave the page, use the Domain and Range Calculator result to answer three quick questions: What was the input? What rule, formula, or method connects the input to the result? What would change if one number in the problem changed? These questions turn a single calculator answer into a reusable math skill.

For homework, write the original problem, the calculator's result, and one short explanation of the method in your notebook. For test review, cover the result and try to reproduce the setup on your own. If you can set up a similar problem without looking back at the calculator, you are much closer to owning the skill.