Function Range Finder Calculator
The page stays in a single-column flow, while the input controls shift to three columns on large screens, two on smaller screens, and one on mobile.
Example Data Table
| Function | Chosen Domain | Key Point | Range |
|---|---|---|---|
| f(x) = x² - 4x + 3 | [-3, 5] | Vertex at x = 2 | [-1, 24] |
| f(x) = 2|x - 1| - 3 | [-2, 6] | Corner at x = 1 | [-3, 7] |
| f(x) = 3/(x - 2) + 1 | [0, 5] | Asymptote at x = 2 | (-∞, -0.5] ∪ [2, ∞) |
| f(x) = 2√(x - 1) + 4 | [1, 10] | Restriction x ≥ 1 | [4, 10] |
| f(x) = 5sin(x) | [0, 2π] | Extrema inside interval | [-5, 5] |
Formula Used
General idea: Range means all possible output values produced by a function over a chosen domain.
Closed interval method: Compare endpoint values and any interior extrema, corners, or asymptote-driven branches.
Typical checks: vertex for quadratics, derivative roots for cubics, x = h for absolute value, validity rules for roots and logs, and peak locations for sine or cosine.
- Linear: evaluate domain endpoints.
- Quadratic: test endpoints and x = -b/(2a).
- Cubic: solve 3ax² + 2bx + c = 0, then test valid roots.
- Absolute value: compare endpoints and x = h.
- Square root: restrict to x ≥ h, then test valid endpoints.
- Reciprocal: inspect endpoints and whether x = h splits the domain.
- Exponential and logarithmic: use valid interval limits and domain restrictions.
- Sine and cosine: test endpoints plus interior peaks and troughs.
How to Use This Calculator
- Choose a supported function family from the list.
- Enter the domain start and domain end for your interval.
- Fill in only the coefficients that belong to that function type.
- Set the number of decimal places for rounded display.
- Press Find Range to show the range above the form.
- Review the evaluated domain, range notation, min and max details, and method note.
- Download the output as CSV for records or PDF for reports.
FAQs
1. What does range mean in this calculator?
Range is the complete set of output values a function produces over your selected domain. This tool reports the range with interval notation whenever possible.
2. Why do I need to enter a domain?
Many functions change their range when the input interval changes. A limited domain can remove extreme outputs or create a smaller interval of possible y-values.
3. Does the calculator handle undefined points?
Yes. Reciprocal and logarithmic models check invalid x-values. When the domain crosses an asymptote or boundary, the result includes split or unbounded range notation.
4. How is a quadratic range found?
The calculator checks both endpoints and the vertex. If the vertex lies inside your domain, its y-value can create the minimum or maximum output.
5. Why are some coefficient boxes hidden?
Fields change with the selected function type so the form stays focused. Only the parameters needed for that equation family remain visible.
6. Can I use this for trigonometric functions?
Yes. Sine and cosine are supported. The calculator checks endpoints and interior peak locations to capture the highest and lowest outputs within your interval.
7. What is included in the CSV and PDF export?
Exports include the function type, expression, domain, range, summary details, and sampled x and f(x) values shown in the result section.
8. Is the result exact for every function?
It is exact for the supported checks used here on common families and finite intervals. Always review restrictions and notation for discontinuous cases.