Transformations (NF): "outside acts on y, inside acts on x, and inside does the opposite"
A standard method from More about graphs of functions: the steps.
Steps
| New graph | What happens | Point (a, b) becomes |
|---|---|---|
| y = f(x) + k | up k units | (a, b + k) |
| y = f(x + k) | left k units | (a − k, b) |
| y = kf(x) | stretch along y-axis by k | (a, kb) |
| y = f(kx) | squeeze along x-axis by k (x ÷ k) | (a/k, b) |
| y = −f(x) | reflect in the x-axis | (a, −b) |
| y = f(−x) | reflect in the y-axis | (−a, b) |
Check with one point: the vertex of a parabola is the easiest.
For the whole topic, read More about graphs of functions: key points, common mistakes and how the DSE tests it.