Calculator Inputs
Use the model y = floor(a·x + b) + c. The floor function returns the greatest integer less than or equal to its input.
Example Data Table
Example using y = floor(1.5x + 0.25) - 2 across selected x-values.
| x | 1.5x + 0.25 | floor(1.5x + 0.25) | y |
|---|---|---|---|
| -2.0 | -2.75 | -3 | -5 |
| -1.2 | -1.55 | -2 | -4 |
| -0.1 | 0.10 | 0 | -2 |
| 0.6 | 1.15 | 1 | -1 |
| 1.4 | 2.35 | 2 | 0 |
| 2.1 | 3.40 | 3 | 1 |
Formula Used
y = floor(a·x + b) + cfloor(t) is the greatest integer less than or equal to ta·x + b = k, so x = (k - b) / a for integer k1 / |a| when a ≠ 0The parameter a changes the horizontal size of each step and reverses direction when negative. The parameter b shifts where jumps occur. The parameter c shifts every output value vertically by the same amount.
When a = 0, the graph becomes constant because the expression inside the floor function no longer depends on x.
How to Use This Calculator
- Enter values for a, b, and c.
- Choose the graph window with x start and x end.
- Set a plot step. Smaller values create more sample points.
- Add an optional highlight x-value for a single-point inspection.
- Select display precision for neat numeric output.
- Press Graph Floor Function to show the result above the form.
- Review the graph, jump locations, summary cards, and detailed table.
- Use the export buttons to save the table as CSV or the result panel as PDF.
Frequently Asked Questions
1) What does the floor function do?
It maps any real number to the greatest integer less than or equal to that number. For example, floor(3.9) is 3, and floor(-1.2) is -2.
2) Why does the graph look like steps?
The output stays constant over intervals, then changes suddenly when the inside expression reaches the next integer. That makes horizontal segments separated by jumps.
3) What happens when a is negative?
A negative inside scale flips the graph horizontally in behavior. As x increases, the inside expression decreases, so the steps descend instead of rising.
4) What if a equals zero?
Then the inside expression becomes constant. The floor result is fixed, so the graph is a single horizontal line across the full x-window.
5) How do I find the width of each step?
For y = floor(a·x + b) + c with a not zero, the typical horizontal width is 1 divided by the absolute value of a. Larger |a| means narrower steps.
6) Why are some jump locations fractional?
Jumps happen when a·x + b equals an integer. Solving x = (k - b)/a often produces fractional x-values, depending on a, b, and the integer k.
7) Does a smaller plot step improve the graph?
Yes. Smaller steps sample the function more densely and show changes more clearly. Very tiny steps, however, increase table size and calculation load.
8) Is this the same as the greatest integer function?
Yes. In most textbooks, the floor function and greatest integer function refer to the same operation.