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Funktion: f(x) = (x-5)2/4 + 1, Df = R, Wf = [-8; +∞), allgemeine Parabel (Scheitelform), Funktion achsensymmetrisch zur Senkrechten x = 5, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 442 | -60 | 4 | 0 | |
| -9.5 | 412.5 | -58 | 4 | 0 | |
| -9 | 384 | -56 | 4 | 0 | |
| -8.5 | 356.5 | -54 | 4 | 0 | |
| -8 | 330 | -52 | 4 | 0 | |
| -7.5 | 304.5 | -50 | 4 | 0 | |
| -7 | 280 | -48 | 4 | 0 | |
| -6.5 | 256.5 | -46 | 4 | 0 | |
| -6 | 234 | -44 | 4 | 0 | |
| -5.5 | 212.5 | -42 | 4 | 0 | |
| -5 | 192 | -40 | 4 | 0 | |
| -4.5 | 172.5 | -38 | 4 | 0 | |
| -4 | 154 | -36 | 4 | 0 | |
| -3.5 | 136.5 | -34 | 4 | 0 | |
| -3 | 120 | -32 | 4 | 0 | |
| -2.5 | 104.5 | -30 | 4 | 0 | |
| -2 | 90 | -28 | 4 | 0 | |
| -1.5 | 76.5 | -26 | 4 | 0 | |
| -1 | 64 | -24 | 4 | 0 | |
| -0.5 | 52.5 | -22 | 4 | 0 | |
| 0 | 42 | -20 | 4 | 0 | Schnittpunkt Sy(0|42) |
| 0.5 | 32.5 | -18 | 4 | 0 | |
| 1 | 24 | -16 | 4 | 0 | |
| 1.5 | 16.5 | -14 | 4 | 0 | |
| 2 | 10 | -12 | 4 | 0 | |
| 2.5 | 4.5 | -10 | 4 | 0 | |
| 3 | 0 | -8 | 4 | 0 | Nullstelle N(3|0) |
| 3.5 | -3.5 | -6 | 4 | 0 | |
| 4 | -6 | -4 | 4 | 0 | |
| 4.5 | -7.5 | -2 | 4 | 0 | |
| 5 | -8 | 0 | 4 | 0 | Tiefpunkt T(5|-8) |
| 5.5 | -7.5 | 2 | 4 | 0 | |
| 6 | -6 | 4 | 4 | 0 | |
| 6.5 | -3.5 | 6 | 4 | 0 | |
| 7 | 0 | 8 | 4 | 0 | Nullstelle N(7|0) |
| 7.5 | 4.5 | 10 | 4 | 0 | |
| 8 | 10 | 12 | 4 | 0 | |
| 8.5 | 16.5 | 14 | 4 | 0 | |
| 9 | 24 | 16 | 4 | 0 | |
| 9.5 | 32.5 | 18 | 4 | 0 | |
| 10 | 42 | 20 | 4 | 0 | |
| Graph: | |||||
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Abkürzungen: Df = (maximaler) Definitionsbereich, f(x) = Funktion, f'(x) = 1. Ableitung, f''(x) = 2. Ableitung, f'''(x) = 3. Ableitung, H = Hochpunkt, N = Nullstelle, P = Polstelle, R = reelle Zahlen, T = Tiefpunkt, W = Wendepunkt, WS = Sattelpunkt, Wf = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.
Bearbeiter: Michael Buhlmann