, Df = R\{0; 2}, Wf = R\(0.0359; 6.9641), gebrochen rationale Funktion, x -> -∞: f(x) -> 0.75·x+2 = y als Grenzkurve, x -> +∞: f(x) -> 0.75·x+2 = y als Grenzkurve ->www.michael-buhlmann.de
Funktion: f(x) = , Df = R\{0; 2}, Wf = R\(0.0359; 6.9641), gebrochen rationale Funktion, x -> -∞: f(x) -> 0.75·x+2 = y als Grenzkurve, x -> +∞: f(x) -> 0.75·x+2 = y als Grenzkurve ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -5.8333 | 0.72 | 0 | 0 | |
| -9.5 | -5.4728 | 0.72 | -0.01 | 0 | |
| -9 | -5.1136 | 0.72 | -0.01 | 0 | |
| -8.5 | -4.756 | 0.71 | -0.01 | 0 | |
| -8 | -4.4 | 0.71 | -0.01 | 0 | |
| -7.5 | -4.0461 | 0.71 | -0.01 | 0 | |
| -7 | -3.6944 | 0.7 | -0.01 | 0 | |
| -6.5 | -3.3456 | 0.69 | -0.01 | 0 | |
| -6 | -3 | 0.69 | -0.02 | -0.01 | |
| -5.5 | -2.6583 | 0.68 | -0.02 | -0.01 | |
| -5 | -2.3214 | 0.67 | -0.02 | -0.01 | |
| -4.5 | -1.9904 | 0.66 | -0.03 | -0.01 | |
| -4 | -1.6667 | 0.64 | -0.04 | -0.02 | |
| -3.5 | -1.3523 | 0.62 | -0.05 | -0.03 | |
| -3 | -1.05 | 0.59 | -0.06 | -0.04 | |
| -2.5 | -0.7639 | 0.55 | -0.09 | -0.06 | |
| -2 | -0.5 | 0.5 | -0.13 | -0.09 | |
| -1.5 | -0.2679 | 0.42 | -0.19 | -0.16 | |
| -1 | -0.0833 | 0.31 | -0.3 | -0.3 | |
| -0.67 | -0.0006 | 0.19 | -0.42 | -0.47 | Nullstelle N(-0.67|0) |
| -0.5 | 0.025 | 0.11 | -0.51 | -0.62 | |
| -0.31 | 0.0359 | 0 | -0.65 | -0.85 | Hochpunkt H(-0.31|0.04) |
| 0 | - | - | - | - | Lücke L(0|0) |
| 0.5 | -0.2917 | -1.03 | -2.37 | -4.77 | |
| 1 | -1.25 | -3.25 | -8 | -24.24 | |
| 1.5 | -4.875 | -15.25 | -64.01 | -391.88 | |
| 2 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 2 mit Vorzeichenwechsel: x -> 2-: f(x) -> -∞, x -> 2+: f(x) -> +∞ |
| 2.5 | 11.875 | -15.25 | 64.01 | -376.51 | |
| 3 | 8.25 | -3.25 | 8 | -23.76 | |
| 3.5 | 7.2917 | -1.03 | 2.37 | -4.71 | |
| 4 | 7 | -0.25 | 1 | -1.49 | |
| 4.305 | 6.9641 | 0 | 0.65 | -0.85 | Tiefpunkt T(4.31|6.96) |
| 4.5 | 6.975 | 0.11 | 0.51 | -0.61 | |
| 5 | 7.0833 | 0.31 | 0.3 | -0.3 | |
| 5.5 | 7.2679 | 0.42 | 0.19 | -0.16 | |
| 6 | 7.5 | 0.5 | 0.13 | -0.09 | |
| 6.5 | 7.7639 | 0.55 | 0.09 | -0.06 | |
| 7 | 8.05 | 0.59 | 0.06 | -0.04 | |
| 7.5 | 8.3523 | 0.62 | 0.05 | -0.03 | |
| 8 | 8.6667 | 0.64 | 0.04 | -0.02 | |
| 8.5 | 8.9904 | 0.66 | 0.03 | -0.01 | |
| 9 | 9.3214 | 0.67 | 0.02 | -0.01 | |
| 9.5 | 9.6583 | 0.68 | 0.02 | -0.01 | |
| 10 | 10 | 0.69 | 0.02 | -0.01 | |
| Graph: | |||||
 | |||||
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