, Df = R\{0}, Wf = R, gebrochen rationale Funktion, x -> -∞: f(x) -> 0.25·x = y als Grenzkurve, x -> +∞: f(x) -> 0.25·x = y als Grenzkurve ->www.michael-buhlmann.de
Funktion: f(x) = , Df = R\{0}, Wf = R, gebrochen rationale Funktion, x -> -∞: f(x) -> 0.25·x = y als Grenzkurve, x -> +∞: f(x) -> 0.25·x = y als Grenzkurve ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -2.52 | 0.25 | 0 | 0 | |
| -9.5 | -2.3972 | 0.25 | 0 | 0 | |
| -9 | -2.2747 | 0.24 | 0 | 0 | |
| -8.5 | -2.1527 | 0.24 | 0 | 0 | |
| -8 | -2.0312 | 0.24 | 0 | 0 | |
| -7.5 | -1.9106 | 0.24 | 0 | 0 | |
| -7 | -1.7908 | 0.24 | 0 | 0 | |
| -6.5 | -1.6723 | 0.24 | -0.01 | 0 | |
| -6 | -1.5556 | 0.23 | -0.01 | -0.01 | |
| -5.5 | -1.4411 | 0.23 | -0.01 | -0.01 | |
| -5 | -1.33 | 0.22 | -0.02 | -0.02 | |
| -4.5 | -1.2238 | 0.21 | -0.03 | -0.03 | |
| -4 | -1.125 | 0.19 | -0.05 | -0.05 | |
| -3.5 | -1.0383 | 0.16 | -0.08 | -0.09 | |
| -3 | -0.9722 | 0.1 | -0.15 | -0.2 | |
| -2.52 | -0.9449 | 0 | -0.3 | -0.47 | Hochpunkt H(-2.52|-0.94) |
| -2.5 | -0.945 | -0.01 | -0.31 | -0.49 | |
| -2 | -1 | -0.25 | -0.75 | -1.5 | |
| -1.5 | -1.2639 | -0.94 | -2.37 | -6.33 | |
| -1 | -2.25 | -3.75 | -12 | -48.12 | |
| -0.5 | -8.125 | -31.75 | -192 | -1543.73 | |
| -0.001 | -2000000.0002 | -Infinity | -Infinity | Infinity | Hochpunkt H(0|-2000000) |
| 0 | -Infinity | 0.25 | Infinity | -Infinity | Senkrechte Asymptote/Pol x = 0 ohne Vorzeichenwechsel: x -> 0-: f(x) -> -∞, x -> 0+: f(x) -> -∞ |
| 0.5 | -7.875 | 32.25 | -192 | 1528.37 | |
| 1 | -1.75 | 4.25 | -12 | 47.88 | |
| 1.5 | -0.5139 | 1.44 | -2.37 | 6.31 | |
| 2 | 0 | 0.75 | -0.75 | 1.5 | Nullstelle N(2|0) |
| 2.5 | 0.305 | 0.51 | -0.31 | 0.49 | |
| 3 | 0.5278 | 0.4 | -0.15 | 0.2 | |
| 3.5 | 0.7117 | 0.34 | -0.08 | 0.09 | |
| 4 | 0.875 | 0.31 | -0.05 | 0.05 | |
| 4.5 | 1.0262 | 0.29 | -0.03 | 0.03 | |
| 5 | 1.17 | 0.28 | -0.02 | 0.02 | |
| 5.5 | 1.3089 | 0.27 | -0.01 | 0.01 | |
| 6 | 1.4444 | 0.27 | -0.01 | 0.01 | |
| 6.5 | 1.5777 | 0.26 | -0.01 | 0 | |
| 7 | 1.7092 | 0.26 | 0 | 0 | |
| 7.5 | 1.8394 | 0.26 | 0 | 0 | |
| 8 | 1.9688 | 0.26 | 0 | 0 | |
| 8.5 | 2.0973 | 0.26 | 0 | 0 | |
| 9 | 2.2253 | 0.26 | 0 | 0 | |
| 9.5 | 2.3528 | 0.25 | 0 | 0 | |
| 10 | 2.48 | 0.25 | 0 | 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