| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2007 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Asymptotes after transformation |
| Difficulty | Moderate -0.8 This is a straightforward C1 transformation question requiring a vertical translation of a standard reciprocal function, identifying asymptotes (which shift predictably), and finding an axis intercept by substitution. All steps are routine applications of basic transformation rules with no problem-solving insight needed. |
| Spec | 1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| - Shape of \(f(x)\) | B1 | |
| - Moved up ↑ | M1 | |
| - Asymptotes: \(y = 3\) | B1 | |
| - \(x = 0\) (Allow "y-axis") | B1 | (\(y \neq 3\) is B0, \(x \neq 0\) is B0) |
| Answer | Marks | Guidance |
|---|---|---|
| (b) \(\frac{1}{x} + 3 = 0\) | M1 | No variations accepted. |
| \(x = -\frac{1}{3}\) (or −0.33 …) | A1 | Decimal answer requires at least 2 d.p. |
**(a)**
- Shape of $f(x)$ | B1 |
- Moved up ↑ | M1 |
- Asymptotes: $y = 3$ | B1 |
- $x = 0$ (Allow "y-axis") | B1 | ($y \neq 3$ is B0, $x \neq 0$ is B0)
**Total: 4 marks**
**(b)** $\frac{1}{x} + 3 = 0$ | M1 | No variations accepted.
$x = -\frac{1}{3}$ (or −0.33 …) | A1 | Decimal answer requires at least 2 d.p.
**Total: 2 marks**
**Overall: 6 marks**
**Guidance:**
- (a) B1: Shape requires both branches and no obvious "overlap" with the asymptotes. The curve may bend away from the asymptote a little at the end. Sufficient curve must be seen to suggest the asymptotic behaviour, both horizontal and vertical.
- M1: Evidence of an upward translation parallel to the y-axis. The shape of the graph can be wrong, but the complete graph (both branches if they have 2 branches) must be translated upwards. This mark can be awarded generously by implication where the graph drawn is an upward translation of another standard curve (but not a straight line).
- The B marks for asymptote equations are independent of the graph. Ignore extra asymptote equations, if seen.
- (b) Correct answer with no working scores both marks. The answer may be seen on the sketch in part (a). Ignore any attempts to find an intersection with the y-axis.
---3. Given that $\quad \mathrm { f } ( x ) = \frac { 1 } { x } , \quad x \neq 0$,
\begin{enumerate}[label=(\alph*)]
\item sketch the graph of $y = \mathrm { f } ( x ) + 3$ and state the equations of the asymptotes.
\item Find the coordinates of the point where $y = \mathrm { f } ( x ) + 3$ crosses a coordinate axis.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2007 Q3 [6]}}