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Funktion: f(x) = , Df = R\{0}, Wf = R, gebrochen rationale Funktion, Funktion achsensymmetrisch zur Senkrechten x = 0, x -> -∞: f(x) -> x2 = y als Grenzkurve, x -> +∞: f(x) -> x2 = y als Grenzkurve ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 99.84 | -20.03 | 1.99 | 0 | |
-9.5 | 90.0727 | -19.04 | 1.99 | 0 | |
-9 | 80.8025 | -18.04 | 1.99 | -0.01 | |
-8.5 | 72.0285 | -17.05 | 1.98 | -0.01 | |
-8 | 63.75 | -16.06 | 1.98 | -0.01 | |
-7.5 | 55.9656 | -15.08 | 1.97 | -0.02 | |
-7 | 48.6735 | -14.09 | 1.96 | -0.02 | |
-6.5 | 41.8713 | -13.12 | 1.95 | -0.03 | |
-6 | 35.5556 | -12.15 | 1.93 | -0.05 | |
-5.5 | 29.7211 | -11.19 | 1.9 | -0.08 | |
-5 | 24.36 | -10.26 | 1.85 | -0.12 | |
-4.5 | 19.4599 | -9.35 | 1.77 | -0.21 | |
-4 | 15 | -8.5 | 1.62 | -0.38 | |
-3.5 | 10.9439 | -7.75 | 1.36 | -0.73 | |
-3 | 7.2222 | -7.19 | 0.81 | -1.58 | |
-2.633 | 4.6248 | -7.02 | 0 | -3.04 | Wendepunkt W(-2.63|4.62) |
-2.5 | 3.69 | -7.05 | -0.46 | -3.94 | |
-2 | 0 | -8 | -4 | -12.02 | Nullstelle N(-2|0) |
-1.5 | -4.8611 | -12.48 | -16.96 | -50.65 | |
-1 | -15 | -34 | -94 | -384.96 | |
-0.5 | -63.75 | -257 | -1534.01 | -12349.81 | |
0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 ohne Vorzeichenwechsel: x -> 0-: f(x) -> -∞, x -> 0+: f(x) -> -∞ |
0.5 | -63.75 | 257 | -1534.01 | 12226.93 | |
1 | -15 | 34 | -94 | 383.04 | |
1.5 | -4.8611 | 12.48 | -16.96 | 50.48 | |
2 | 0 | 8 | -4 | 11.99 | Nullstelle N(2|0) |
2.5 | 3.69 | 7.05 | -0.46 | 3.93 | |
2.632 | 4.6178 | 7.02 | 0 | 3.04 | Wendepunkt W(2.63|4.62) |
3 | 7.2222 | 7.19 | 0.81 | 1.58 | |
3.5 | 10.9439 | 7.75 | 1.36 | 0.73 | |
4 | 15 | 8.5 | 1.62 | 0.37 | |
4.5 | 19.4599 | 9.35 | 1.77 | 0.21 | |
5 | 24.36 | 10.26 | 1.85 | 0.12 | |
5.5 | 29.7211 | 11.19 | 1.9 | 0.08 | |
6 | 35.5556 | 12.15 | 1.93 | 0.05 | |
6.5 | 41.8713 | 13.12 | 1.95 | 0.03 | |
7 | 48.6735 | 14.09 | 1.96 | 0.02 | |
7.5 | 55.9656 | 15.08 | 1.97 | 0.02 | |
8 | 63.75 | 16.06 | 1.98 | 0.01 | |
8.5 | 72.0285 | 17.05 | 1.98 | 0.01 | |
9 | 80.8025 | 18.04 | 1.99 | 0.01 | |
9.5 | 90.0727 | 19.04 | 1.99 | 0.01 | |
10 | 99.84 | 20.03 | 1.99 | 0 | |
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