| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Topic | Modulus function |
| Type | Transformations of modulus graphs from given f(x) sketch |
| Difficulty | Standard +0.3 This question involves standard transformations of a modulus function graph (horizontal translation and even function composition) and solving a linear-modulus equation. Part (c) requires simple substitution into the given formula, while part (d) involves solving |x-1| - 2 = 5x by considering two cases. All techniques are routine for C3 level with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02w Graph transformations: simple transformations of f(x) |
6.
\begin{figure}[h]
\begin{center}
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\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{933ec0b9-3496-455e-9c2c-2612e84f63ff-02_371_643_338_1852}
\end{center}
\end{figure}
Figure 1 shows part of the graph of $y = \mathrm { f } ( x ) , x \in \mathbb { R }$. The graph consists of two line segments that meet at the point $( 1 , a ) , a < 0$. One line meets the $x$-axis at $( 3,0 )$. The other line meets the $x$-axis at $( - 1,0 )$ and the $y$-axis at $( 0 , b ) , b < 0$.
In separate diagrams, sketch the graph with equation
\begin{enumerate}[label=(\alph*)]
\item $y = \mathrm { f } ( x + 1 )$,
\item $y = \mathrm { f } ( | x | )$.
Indicate clearly on each sketch the coordinates of any points of intersection with the axes.\\
Given that $\mathrm { f } ( x ) = | x - 1 | - 2$, find
\item the value of $a$ and the value of $b$,
\item the value of $x$ for which $\mathrm { f } ( x ) = 5 x$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q6 [15]}}