Calculator Form
Example Data Table
| Graph case | Entered details | Expected domain | Expected range |
|---|---|---|---|
| Line with arrows | x: -∞ to ∞, y: -∞ to ∞ | (-∞, ∞) | (-∞, ∞) |
| Square root curve | x starts at 3 closed, y starts at 0 closed | [3, ∞) | [0, ∞) |
| Rational graph | x: -∞ to ∞, vertical asymptote x = 2 | (-∞, 2) ∪ (2, ∞) | Depends on the graph |
| Open segment | x: -4 open to 6 open, y: -2 open to 5 open | (-4, 6) | (-2, 5) |
Formula Used
Domain: all x-values touched by the graph.
Range: all y-values touched by the graph.
Interval rule: start with the lowest and highest visible values. Then remove holes, asymptotes, gaps, and open endpoints.
Endpoint rule: use brackets for included endpoints. Use parentheses for excluded endpoints and infinity.
Union rule: when a gap splits values, join the separate intervals with ∪.
How To Use This Calculator
- Read the graph from left to right for the domain.
- Read the graph from bottom to top for the range.
- Enter each boundary value and choose open or closed.
- Add vertical asymptotes, holes, and missing x-values.
- Add missing y-values only when that height never appears.
- Submit the form to see interval notation above the form.
- Use CSV or PDF download options for saving the result.
Understanding Domain and Range From a Graph
The domain tells which input values are allowed. On a graph, these values are read along the horizontal axis. You scan from the far left point to the far right point. Then you note gaps, holes, and vertical breaks. A closed dot includes an endpoint. An open dot does not include it.
The range tells which output values occur. These values are read along the vertical axis. You scan from the lowest point to the highest point. Then you remove any missing heights. A graph may reach a height more than once. In that case, one removed point may not remove that y-value. Use the hole option only when that height is truly missing.
This calculator helps organize that reading process. Enter the visible left and right x-limits. Choose whether each endpoint is open or closed. Do the same for the bottom and top y-limits. Add excluded x-values for vertical asymptotes, jumps, or breaks. Add excluded y-values when a horizontal level is never touched. The tool converts those details into interval notation.
Interval notation is compact. Parentheses show values that are not included. Brackets show values that are included. Infinity always uses parentheses. A union symbol joins separate intervals. Point notation is used when only one value remains.
Graph domain and range questions need care. A curve can continue beyond the window. Arrows usually mean the graph goes on forever. Asymptotes mark lines the graph approaches but does not cross, unless the graph actually touches that level elsewhere. Always inspect arrows, dots, and labels before entering values.
Use the example table as a model. It shows common graph cases. Lines often have all real domains and ranges. Square root graphs often start at one point and extend one way. Rational graphs often exclude vertical asymptotes from the domain. Quadratics may have all real x-values but only a bounded range.
For best results, zoom into endpoints. Check whether dots are open or closed. List every break separately. Review the final interval before exporting. Save the CSV for spreadsheet work. Use the PDF button for a neat study record. Recheck unusual graphs with your teacher or textbook.
This prevents common notation mistakes during exams too.
FAQs
What is the domain of a graph?
The domain is the set of all x-values where the graph exists. Read it from left to right along the x-axis.
What is the range of a graph?
The range is the set of all y-values reached by the graph. Read it from bottom to top along the y-axis.
Should infinity use a bracket?
No. Infinity is never an included endpoint. Always use parentheses with ∞ or -∞ in interval notation.
How do holes affect the domain?
A hole usually removes its x-value from the domain. If another point exists at the same x-value, do not remove it.
How do holes affect the range?
A hole removes its y-value only when no other graph point reaches that same height. Check the full graph first.
What does a vertical asymptote do?
A vertical asymptote often removes an x-value from the domain. Enter that value in the vertical asymptote box.
What does a horizontal asymptote do?
A horizontal asymptote may or may not be excluded from the range. Use the checkbox only when the graph never touches that y-value.
Can this handle piecewise graphs?
Yes. Enter the total x-span, total y-span, and every missing value. Use isolated points for single separate dots.