Every restriction listed.
Denominators set to zero, radicands set non-negative, log arguments set positive. AskSia checks each and reports excluded values.
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Range and Domain Solver
Domain and range. Found, explained, graphed.
Type your function or snap a worksheet. AskSia checks every place the function could break (zero denominators, negative square roots, log arguments at or below zero), states the domain in interval notation, then analyzes end behavior and extrema to give you the range. The graph shows asymptotes and any excluded points.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
4.9 / 5 · trusted by 2M+ students · 50M+ problems solved
asksia.ai/solver
98% · Verified
Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
How do you find the range and domain?
The domain is the set of inputs for which the function is defined. Find it by listing every restriction: denominators cannot be zero, even-root radicands cannot be negative, and log arguments must be positive. Whatever is left of the real line is the domain. The range is the set of outputs. Find it by analyzing end behavior, finding extrema with calculus or completing the square, and checking continuity. Both domain and range are written in interval notation.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for domain and range.
Every restriction surfaced, every output analyzed.
Asymptotes identified.
Vertical, horizontal, and oblique asymptotes get found and labeled, with the limits that produce them shown.
Asymptotes
Range from behavior.
End behavior, extrema, and continuity give the output set. AskSia uses calculus for differentiable functions and algebra otherwise.
Range analysis
Interval notation native.
Answers appear in interval notation by default, with set-builder notation available on request.
Standard form
Graph included.
The function gets plotted with domain restrictions, asymptotes, and any excluded points clearly marked.
Visual
Piecewise supported.
Piecewise definitions get analyzed piece by piece and combined into a final domain and range.
Piecewise
How It Works
Find domain and range in three steps.
Step 01
Enter the function.
Type, paste, photograph, or speak f(x). AskSia identifies the function type and any places it can fail to be defined.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia analyzes restrictions and behavior.
Every excluded value is computed. End behavior, extrema, and asymptotes determine the range.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Read the answer.
Domain and range appear in interval notation. The graph shows excluded points and asymptotes. Set-builder available on toggle.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
Available On
Solve anywhere
you study.
Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
Web App
Full study studio
Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App
Snap & solve, anywhere
Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
Offline review of saved solutions and flashcards
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98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What range and domain analysis covers.
Rational functions.
Denominator zeros give vertical asymptotes or holes. AskSia distinguishes and excludes appropriately.
Rational
Square root functions.
Radicand >= 0 gives the domain. Range follows from the non-negative output of the square root.
Radical
Logarithmic functions.
Argument > 0 gives the domain. Range is all reals for standard logs.
Logs
Polynomials.
Domain is all reals. Range comes from end behavior and extrema. AskSia uses calculus or completing the square.
Polynomial
Trig functions.
Tangent and secant have excluded values at odd multiples of pi/2. Sine and cosine have bounded range.
Trig
Composite functions.
f(g(x)) has its own domain restrictions that combine the inner and outer restrictions. AskSia handles the composition carefully.
Composition
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
What is the difference between a hole and a vertical asymptote?
Both come from denominator zeros, but a hole occurs when the same factor cancels with the numerator (a removable discontinuity), while a vertical asymptote occurs when the denominator factor does not cancel. AskSia factors numerator and denominator, cancels common factors, and reports the cancelled ones as holes and the remaining denominator zeros as vertical asymptotes.
How is the range of a polynomial found?
For even-degree polynomials, range is bounded above or below by the extremum (minimum if leading coefficient is positive, maximum if negative). For odd degree, range is all real numbers. AskSia computes the extremum by completing the square (quadratics) or by setting the derivative to zero (higher degree).
Can AskSia handle piecewise functions?
Yes. For piecewise definitions, each piece is analyzed for its own domain and range, then combined. AskSia checks continuity at the breakpoints and reports any jumps or excluded points. The graph shows each piece with its endpoint conventions (open or closed dots).
Why are interval and set-builder notation both useful?
Interval notation is compact and standard in algebra and calculus. Set-builder notation is more flexible for unusual domains (like 'all reals except where sin x = 0'). AskSia gives interval notation by default and switches to set-builder when the domain or range cannot be written cleanly as an interval union.
How accurate is AskSia?
AskSia hits 98% accuracy on standard high school and college coursework, measurably higher than ChatGPT, Photomath, and Symbolab on the same problem sets. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
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Every restriction. Every output value. Mapped out.
Join 2M+ students using AskSia to find domain and range with full step-by-step analysis. Interval notation, asymptotes, excluded points, and a labeled graph on every solve.
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