Graphical Transformations for IPY3Y4 Math
Download printable cheat-sheet (CC-BY 4.0)24 Aug 2025, 16:00 Z
y = f (x)
| Number | Transformation | Effect on graph |
| 1 | y = f (x) + a | Translation of a units along the y-axis |
| 2 | y = f (x + a) | Translation of -a units along the x-axis |
| 3 | y = af(x) | Scaling parallel to y-axis by a factor of a units |
| 4 | y = -f(ax) | Scaling parallel to x-axis by a factor of 1/a units |
| 5 | y = -f(x) | Reflection about the x-axis |
| 6 | y = f(-x) | Reflection about the y-axis |
In layman terms: 1) move the graph up or down by a units
2) move the graph right or left by a units
3) multiply all y-coordinate values by a
4) multiply all x-coordinate values by 1/a
5) multiply all y-coordinate values by negative (negative values move up, positive values move down)
6) multiply all x-coordinate values by negative (negative values move to the right, positive values move to the left)
Rule of thumb: translation and scaling of x-axis is inverted, i.e. when you add by a, you move left by a, when you multiply by a, you divide the value by a. for y-axis it works normally
multiple transformations (priority list is to work inside the bracket first and branch out):
| Number | Transformation | Effects on graph |
| 1 | y = cf(bx+a) + d | AMMA rule (add, multiply x-axis, then multiply, add y-axis) |
| translation of -a units along the x-axis | ||
| scaling parallel to x-axis by factor of 1/b units | ||
| scaling parallel to y-axis by a factor of c units | ||
| translation of a units along the y-axis |
