, Df = R\{2}, Wf = R, gebrochen rationale Funktion, x -> -∞: f(x) -> 2x = y als Grenzkurve, x -> +∞: f(x) -> 2x = y als Grenzkurve ->www.michael-buhlmann.de
Funktion: f(x) = , Df = R\{2}, Wf = R, gebrochen rationale Funktion, x -> -∞: f(x) -> 2x = y als Grenzkurve, x -> +∞: f(x) -> 2x = y als Grenzkurve ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -20.0214 | 2 | 0 | 0 | |
| -9.5 | -19.023 | 2 | 0 | 0 | |
| -9 | -18.0248 | 2 | 0 | 0 | |
| -8.5 | -17.0268 | 2 | 0 | 0 | |
| -8 | -16.029 | 2 | 0 | 0 | |
| -7.5 | -15.0315 | 1.99 | 0 | 0 | |
| -7 | -14.0343 | 1.99 | 0 | 0 | |
| -6.5 | -13.0375 | 1.99 | 0 | 0 | |
| -6 | -12.041 | 1.99 | 0 | 0 | |
| -5.5 | -11.045 | 1.99 | 0 | 0 | |
| -5 | -10.0496 | 1.99 | 0 | 0 | |
| -4.5 | -9.0546 | 1.99 | 0 | 0 | |
| -4 | -8.0602 | 1.99 | 0 | 0 | |
| -3.502 | -7.0701 | 1.99 | 0 | 0 | Wendepunkt W(-3.5|-7.07) |
| -3.5 | -7.0661 | 1.99 | 0 | 0 | |
| -3 | -6.072 | 1.99 | 0 | 0.01 | |
| -2.5 | -5.0768 | 1.99 | 0.01 | 0.03 | |
| -2 | -4.0781 | 2 | 0.04 | 0.07 | |
| -1.5 | -3.07 | 2.03 | 0.09 | 0.18 | |
| -1 | -2.037 | 2.11 | 0.25 | 0.51 | |
| -0.5 | -0.936 | 2.33 | 0.74 | 1.72 | |
| -0.13 | 0 | 2.78 | 1.84 | 4.89 | Nullstelle N(-0.13|0) |
| 0 | 0.375 | 3.06 | 2.63 | 7.34 | Schnittpunkt Sy(0|0.38) |
| 0.5 | 2.4815 | 6.15 | 12.64 | 45.49 | |
| 1 | 9 | 27 | 108 | 567.5 | |
| 1.5 | 75 | 466.03 | 3840.16 | 39650.96 | |
| 2 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 2 mit Vorzeichenwechsel: x -> 2-: f(x) -> +∞, x -> 2+: f(x) -> -∞ |
| 2.5 | -99 | 594.03 | -4608.18 | 44781.79 | |
| 3 | -9 | 43 | -156 | 751.59 | |
| 3.346 | 0 | 15.33 | -37.19 | 132.14 | Nullstelle N(3.35|0) |
| 3.5 | 1.963 | 10.89 | -22.12 | 70.31 | |
| 4 | 5.625 | 5.06 | -5.63 | 13.27 | |
| 4.5 | 7.656 | 3.36 | -1.97 | 3.68 | |
| 5 | 9.1481 | 2.7 | -0.84 | 1.3 | |
| 5.5 | 10.4169 | 2.41 | -0.41 | 0.54 | |
| 6 | 11.5781 | 2.25 | -0.22 | 0.25 | |
| 6.5 | 12.6818 | 2.17 | -0.13 | 0.13 | |
| 7 | 13.752 | 2.12 | -0.08 | 0.07 | |
| 7.5 | 14.8017 | 2.08 | -0.05 | 0.04 | |
| 8 | 15.838 | 2.06 | -0.04 | 0.03 | |
| 8.5 | 16.8653 | 2.05 | -0.02 | 0.02 | |
| 9 | 17.8863 | 2.04 | -0.02 | 0.01 | |
| 9.5 | 18.9028 | 2.03 | -0.01 | 0.01 | |
| 10 | 19.916 | 2.02 | -0.01 | 0.01 | |
| Graph: | |||||
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Graph(en) der Asymptote(n), Grenzkurve(n).
Abkürzungen: Df = (maximaler) Definitionsbereich, f(x) = Funktion, f'(x) = 1. Ableitung, f''(x) = 2. Ableitung, f'''(x) = 3. Ableitung, H = Hochpunkt, L = Lücke, N = Nullstelle, P = Polstelle, R = reelle Zahlen, S = Sprungstelle, T = Tiefpunkt, W = Wendepunkt, WS = Sattelpunkt, Wf = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.
Bearbeiter: Michael Buhlmann