Solve values across four rules with visual feedback. Track boundaries, inclusions, and interval behavior effortlessly. Build confidence through examples, exports, formulas, graphs, and FAQs.
Results appear here after each submission.
Enter four rules, define intervals, choose inclusions, and test one x-value.
The graph shows the complete four-piece function over the selected domain.
These sampled points help verify interval switching and function output.
| Sample x | Matched Piece | Interval | f(x) |
|---|---|---|---|
| -10 | None | Outside all defined intervals | Undefined |
| -8.32636 | 1 | (-10, -2) | 70.328268 |
| -6.65272 | 1 | (-10, -2) | 45.258679 |
| -4.979079 | 1 | (-10, -2) | 25.791233 |
| -3.305439 | 1 | (-10, -2) | 11.925929 |
| -1.631799 | 2 | (-2, 1) | -0.263598 |
| 0.041841 | 2 | (-2, 1) | 3.083682 |
| 1.715481 | 3 | (1, 4) | 3.715481 |
| 3.389121 | 3 | (1, 4) | 5.389121 |
| 5.062762 | 4 | (4, 10) | 59.820461 |
| 6.736402 | 4 | (4, 10) | 146.109546 |
| 8.410042 | 4 | (4, 10) | 289.006058 |
A four-piece function selects one rule from four possible rules.
It depends on which interval contains the input value.
f(x) =
{ f₁(x), x in I₁;
f₂(x), x in I₂;
f₃(x), x in I₃;
f₄(x), x in I₄ }
Each interval can be open, closed, or mixed.
The calculator checks bounds and inclusion settings first.
Then it evaluates only the matching expression for x.
If x fits no interval, the result is undefined.
It is a function defined by four different expressions. Each expression applies only on its assigned interval. The active formula changes when x crosses a breakpoint.
Inclusions decide whether a boundary value belongs to a piece. A closed endpoint includes the boundary. An open endpoint excludes it. This prevents overlap or ambiguity.
The calculator returns an undefined result. This means the function has no assigned rule at that x-value. The graph also leaves that point empty.
You can enter overlapping intervals, but only the first matching piece is used. For accurate math work, define non-overlapping intervals whenever possible.
You can use x, numbers, parentheses, powers, and common functions like abs, sqrt, sin, cos, tan, log, and exp. Keep expressions algebraic and simple.
Breaks appear where the function is undefined or where no interval covers a plotted x-value. They also help reveal jumps and domain gaps clearly.
The table lists sampled x-values across your graph range. It shows the matched piece, active interval, and output. This helps you validate transitions and rule selection.
Use CSV for spreadsheets, assignment data, and records. Use PDF for sharing a printable summary, graph, and result details with teachers or teammates.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.