Open navigation menu
Loading resource…
Mathematics discovery lab
Change parameters to observe translation, stretch/compression, reflection, domain and range of five basic functions.
Every change uses the same model y = a·f(b(x − h)) + k and updates instantly.
The vertex moves to the image of the point (0; 0), but the opening also depends on both |a| and |b|.
Not every function has a vertex or an axis of symmetry. The square-root and reciprocal functions also do not have the whole real line as their domain.
Curves, characteristic points and asymptotes share one coordinate system.
Drag the background or use the zoom buttons to change the view.
| x | −6 | −4 | −2 | 0 | 2 | 4 | 6 |
|---|---|---|---|---|---|---|---|
| f(x) | 36 | 16 | 4 | 0 | 4 | 16 | 36 |
Action hint: Drag the background to move the view; use zoom or Fit to observe the graph.
|a| stretches/compresses vertically; negative a reflects across Ox. A value of 0 is ignored.
|b| acts horizontally by the reciprocal; negative b reflects across Oy. A value of 0 is ignored.
Positive h in f(x − h) shifts the graph to the right.
Positive k shifts the graph upward.