Lösung Funktionsterme nach Transformationen bestimmen
Zuletzt geändert von Martin Rathgeb am 2025/06/03 21:45
a) \(g(x)=-\frac{2}{x-1}+3\)
b) \(g(x)=-\frac{2}{x-1}-6\)
c) \(g(x)=-\frac{2}{x-1}+3\)
| Schritt | Teilaufgabe a) | Teilaufgabe b) | Teilaufgabe c) |
| Startfunktion | \(f(x) = \frac{1}{x}\) | \(f(x) = \frac{1}{x}\) | \(f(x) = \frac{1}{x}\) |
| 1. Transformation | \(f(x) \rightarrow -\frac{1}{x}\) | \(f(x) \rightarrow \frac{1}{x - 1}\) | \(f(x) \rightarrow \frac{1}{x - 1}\) |
| 2. Transformation | \(-\frac{1}{x} \rightarrow -\frac{2}{x}\) | \(\frac{1}{x - 1} \rightarrow \frac{1}{x - 1} + 3\) | \(\frac{1}{x - 1} \rightarrow \frac{2}{x - 1}\) |
| 3. Transformation | \(-\frac{2}{x} \rightarrow -\frac{2}{x - 1}\) | \(\frac{1}{x - 1} + 3 \rightarrow \frac{2}{x - 1} + 6\) | \(\frac{2}{x - 1} \rightarrow -\frac{2}{x - 1}\) |
| 4. Transformation | \(-\frac{2}{x - 1} \rightarrow g(x) = -\frac{2}{x - 1} + 3\) | \(\frac{2}{x - 1} + 6 \rightarrow g(x) = -\frac{2}{x - 1} - 6\) | \(-\frac{2}{x - 1} \rightarrow g(x) = -\frac{2}{x - 1} + 3\) |