| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Single transformation sketch |
| Difficulty | Moderate -0.8 This is a straightforward graph sketching question testing basic transformations and asymptotes of rational functions. Part (a) is a standard reciprocal square graph, part (b) applies a horizontal translation, and part (c) uses graphical intersection to count roots—all routine A-level techniques requiring minimal problem-solving beyond careful sketching and observation. |
| Spec | 1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02w Graph transformations: simple transformations of f(x) |
The function $f$ is defined by $f(x) = \frac{8}{x^2}$.
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = f(x)$. [2]
\item On a separate set of axes, sketch the graph of $y = f(x - 2)$. Indicate the vertical asymptote and the point where the curve crosses the $y$-axis. [3]
\item Sketch the graphs of $y = \frac{8}{x}$ and $y = \frac{8}{(x-2)^2}$ on the same set of axes.
Hence state the number of roots of the equation $\frac{8}{(x-2)^2} = \frac{8}{x}$. [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2023 Q11 [7]}}