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Funktion: f(x) = x2 + x + 3, Df = R, Wf = [2.75; +∞), verschobene Normalparabel (Normalform; Scheitelform: f(x) = (x+0.5)2 + 2.75), Funktion achsensymmetrisch zur Senkrechten x = -0.5, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 93 | -19 | 2 | 0 | |
| -9.5 | 83.75 | -18 | 2 | 0 | |
| -9 | 75 | -17 | 2 | 0 | |
| -8.5 | 66.75 | -16 | 2 | 0 | |
| -8 | 59 | -15 | 2 | 0 | |
| -7.5 | 51.75 | -14 | 2 | 0 | |
| -7 | 45 | -13 | 2 | 0 | |
| -6.5 | 38.75 | -12 | 2 | 0 | |
| -6 | 33 | -11 | 2 | 0 | |
| -5.5 | 27.75 | -10 | 2 | 0 | |
| -5 | 23 | -9 | 2 | 0 | |
| -4.5 | 18.75 | -8 | 2 | 0 | |
| -4 | 15 | -7 | 2 | 0 | |
| -3.5 | 11.75 | -6 | 2 | 0 | |
| -3 | 9 | -5 | 2 | 0 | |
| -2.5 | 6.75 | -4 | 2 | 0 | |
| -2 | 5 | -3 | 2 | 0 | |
| -1.5 | 3.75 | -2 | 2 | 0 | |
| -1 | 3 | -1 | 2 | 0 | |
| -0.5 | 2.75 | 0 | 2 | 0 | Tiefpunkt T(-0.5|2.75) |
| 0 | 3 | 1 | 2 | 0 | Schnittpunkt Sy(0|3) |
| 0.5 | 3.75 | 2 | 2 | 0 | |
| 1 | 5 | 3 | 2 | 0 | |
| 1.5 | 6.75 | 4 | 2 | 0 | |
| 2 | 9 | 5 | 2 | 0 | |
| 2.5 | 11.75 | 6 | 2 | 0 | |
| 3 | 15 | 7 | 2 | 0 | |
| 3.5 | 18.75 | 8 | 2 | 0 | |
| 4 | 23 | 9 | 2 | 0 | |
| 4.5 | 27.75 | 10 | 2 | 0 | |
| 5 | 33 | 11 | 2 | 0 | |
| 5.5 | 38.75 | 12 | 2 | 0 | |
| 6 | 45 | 13 | 2 | 0 | |
| 6.5 | 51.75 | 14 | 2 | 0 | |
| 7 | 59 | 15 | 2 | 0 | |
| 7.5 | 66.75 | 16 | 2 | 0 | |
| 8 | 75 | 17 | 2 | 0 | |
| 8.5 | 83.75 | 18 | 2 | 0 | |
| 9 | 93 | 19 | 2 | 0 | |
| 9.5 | 102.75 | 20 | 2 | 0 | |
| 10 | 113 | 21 | 2 | 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