Domain & Range Calculator
Algebra, Functions
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Function or math question
Final answer
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Intro: Analyzes f(x) to determine all allowed x-values (domain) and possible y-values (range), with explanations of exclusions.
Worked example
- Find the domain and range of $f(x) = \sqrt{x-3}$.
- We have $f(x)=\sqrt{x-3}$. The expression inside the square root must be nonnegative.
- Set the radicand condition: $x-3 \ge 0$.
- Solve the inequality: $x \ge 3$.
- Thus the domain is all real x such that $x \ge 3$, i.e., $[3, \infty)$.
- Next, analyze the range. For $x \ge 3$, the radicand $x-3$ is at least 0.
- The square root output is always nonnegative: $\sqrt{x-3} \ge 0$ for any x in the domain.
- As x increases beyond 3, $x-3$ can become arbitrarily large, and so can $\sqrt{x-3}$.
- At the left endpoint x = 3, we have $f(3)=\sqrt{3-3}=0$.
- Therefore, y-values start at 0 and increase without bound: the range is $[0, \infty)$.
- Answer: $\boxed{\text{Domain}=[3,\infty),\; \text{Range}=[0,\infty).}$
FAQs
Can it always find an exact range?
For many standard functions (polynomials, rationals, roots, logs, etc.), yes. Some complicated expressions may need interval checking or graph-based hints.
Why use Mathix for domain and range?
- Identify domain restrictions caused by square roots, denominators, and logarithms.
- Find the range by analyzing possible output values and function behavior.
- Receive answers in clear interval notation with excluded values explained.
- Check important boundaries, asymptotes, endpoints, and discontinuities.
How to find the domain and range of a function
- Enter a function using x.
- Run the calculator to identify the domain and range.
- Review the answer in interval notation.
- Check the explanation for restrictions and excluded values.