, Df = R, Wf = [-2.25; 1), gebrochen rationale Funktion, Funktion achsensymmetrisch zur Senkrechten x = 0, x -> -∞: f(x) -> 1 = y als Grenzkurve, x -> +∞: f(x) -> 1 = y als Grenzkurve ->www.michael-buhlmann.de
Funktion: f(x) = , Df = R, Wf = [-2.25; 1), gebrochen rationale Funktion, Funktion achsensymmetrisch zur Senkrechten x = 0, x -> -∞: f(x) -> 1 = y als Grenzkurve, x -> +∞: f(x) -> 1 = y als Grenzkurve ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 0.875 | -0.02 | -0.01 | 0 | |
| -9.5 | 0.8621 | -0.03 | -0.01 | 0 | |
| -9 | 0.8471 | -0.03 | -0.01 | 0 | |
| -8.5 | 0.8295 | -0.04 | -0.01 | -0.01 | |
| -8 | 0.8088 | -0.04 | -0.02 | -0.01 | |
| -7.5 | 0.7842 | -0.05 | -0.02 | -0.01 | |
| -7 | 0.7547 | -0.06 | -0.02 | -0.01 | |
| -6.5 | 0.7189 | -0.08 | -0.03 | -0.02 | |
| -6 | 0.675 | -0.1 | -0.04 | -0.02 | |
| -5.5 | 0.6204 | -0.12 | -0.06 | -0.03 | |
| -5 | 0.5517 | -0.15 | -0.08 | -0.05 | |
| -4.5 | 0.4639 | -0.2 | -0.1 | -0.07 | |
| -4 | 0.35 | -0.26 | -0.14 | -0.09 | |
| -3.5 | 0.2 | -0.34 | -0.2 | -0.13 | |
| -3 | 0 | -0.46 | -0.27 | -0.16 | Nullstelle N(-3|0) |
| -2.5 | -0.2683 | -0.62 | -0.36 | -0.16 | |
| -2 | -0.625 | -0.81 | -0.41 | 0 | |
| -1.5 | -1.08 | -1 | -0.29 | 0.54 | |
| -1.16 | -1.4319 | -1.06 | 0 | 1.19 | Wendepunkt W(-1.16|-1.43) |
| -1 | -1.6 | -1.04 | 0.21 | 1.51 | |
| -0.5 | -2.0588 | -0.72 | 1.1 | 1.79 | |
| 0 | -2.25 | 0 | 1.62 | -0.02 | Schnittpunkt Sy(0|-2.25) = Tiefpunkt T(0|-2.25) |
| 0.5 | -2.0588 | 0.72 | 1.1 | -1.8 | |
| 1 | -1.6 | 1.04 | 0.21 | -1.49 | |
| 1.16 | -1.4319 | 1.06 | 0 | -1.19 | Wendepunkt W(1.16|-1.43) |
| 1.5 | -1.08 | 1 | -0.29 | -0.53 | |
| 2 | -0.625 | 0.81 | -0.41 | 0 | |
| 2.5 | -0.2683 | 0.62 | -0.36 | 0.16 | |
| 3 | 0 | 0.46 | -0.27 | 0.16 | Nullstelle N(3|0) |
| 3.5 | 0.2 | 0.34 | -0.2 | 0.13 | |
| 4 | 0.35 | 0.26 | -0.14 | 0.09 | |
| 4.5 | 0.4639 | 0.2 | -0.1 | 0.07 | |
| 5 | 0.5517 | 0.15 | -0.08 | 0.05 | |
| 5.5 | 0.6204 | 0.12 | -0.06 | 0.03 | |
| 6 | 0.675 | 0.1 | -0.04 | 0.02 | |
| 6.5 | 0.7189 | 0.08 | -0.03 | 0.02 | |
| 7 | 0.7547 | 0.06 | -0.02 | 0.01 | |
| 7.5 | 0.7842 | 0.05 | -0.02 | 0.01 | |
| 8 | 0.8088 | 0.04 | -0.02 | 0.01 | |
| 8.5 | 0.8295 | 0.04 | -0.01 | 0.01 | |
| 9 | 0.8471 | 0.03 | -0.01 | 0 | |
| 9.5 | 0.8621 | 0.03 | -0.01 | 0 | |
| 10 | 0.875 | 0.02 | -0.01 | 0 | |
| 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