| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Multiple separate transformations (sketch-based, modulus involved) |
| Difficulty | Standard +0.3 This is a standard C3 transformation question requiring application of three common transformations (horizontal translation, absolute value of function, absolute value of input). While it requires careful tracking of key points through each transformation, the transformations themselves are routine textbook material with no novel problem-solving required. The 10 marks reflect the bookwork nature rather than conceptual difficulty. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
\includegraphics{figure_1}
Figure 1 shows a sketch of the curve with equation $y = f(x), -1 \leq x \leq 3$. The curve touches the $x$-axis at the origin $O$, crosses the $x$-axis at the point $A(2, 0)$ and has a maximum at the point $B(\frac{4}{3}, 1)$.
In separate diagrams, show a sketch of the curve with equation
\begin{enumerate}[label=(\alph*)]
\item $y = f(x + 1)$, [3]
\item $y = |f(x)|$, [3]
\item $y = f(|x|)$, [4]
\end{enumerate}
marking on each sketch the coordinates of points at which the curve
\begin{enumerate}[label=(\roman*)]
\item has a turning point,
\item meets the $x$-axis.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q27 [10]}}