Transform graphs with intuitive controls and previews. See equations, points, and domains update after changes. Plot original and transformed curves for faster visual understanding.
The page stays in a single vertical flow, while the calculator fields use 3 columns on large screens, 2 on medium, and 1 on mobile.
a changes vertical size. If |a| > 1, the graph stretches vertically. If 0 < |a| < 1, it compresses vertically.
b changes horizontal size through the input. If b > 1, the graph compresses horizontally. If 0 < b < 1, it stretches horizontally.
h shifts the graph right when positive and left when negative. k shifts the graph up when positive and down when negative.
sx equals -1 for reflection across the x-axis, otherwise 1. sy equals -1 for reflection across the y-axis, otherwise 1.
Example shown for the quadratic parent function with a = 2, b = 1, h = 1, and k = 3, giving y = 2(x - 1)² + 3.
| x | Parent y = x² | Transformed y = 2(x - 1)² + 3 |
|---|---|---|
| -1 | 1 | 11 |
| 0 | 0 | 5 |
| 1 | 1 | 3 |
| 2 | 4 | 5 |
| 3 | 9 | 11 |
It applies shifts, stretches, compressions, and reflections to a chosen parent function. The calculator then shows the transformed equation, graph, domain, range, mapped reference points, and a sample result table.
The value a changes the output height. Large absolute values create vertical stretching. Values between zero and one create vertical compression. A negative effective output flips the graph across the x-axis.
The value b affects the input before the parent function is evaluated. When b is greater than one, the graph compresses horizontally. When b is between zero and one, the graph stretches horizontally.
Inside-function changes work in the opposite visual direction. So x − h moves the graph right by h units, while x + h moves it left by h units.
Yes. Square root and reciprocal functions have domain restrictions. The calculator respects those conditions, avoids undefined points, and reports the transformed domain in the results.
Yes. The Plotly graph shows both curves together. This makes it easier to see how each parameter changes position, width, direction, and symmetry.
They show how key parent-function points move after transformation. These points help confirm the graph visually and are useful when checking vertex, intercept, or turning-point behavior.
Yes. The calculator includes CSV and PDF download options. These exports contain the rule, summary details, and numeric result tables for later use or sharing.
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.