| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Modulus function |
| Type | Solve |f(x)| compared to |g(x)| with parameters: sketch then solve |
| Difficulty | Moderate -0.3 This is a straightforward modulus function question requiring standard sketching techniques and solving a linear equation with modulus. Part (a) is routine graph sketching, part (b) applies a horizontal stretch (standard transformation), and part (c) involves solving |2x-a|=x/2 by considering two cases. The algebra is simple once the modulus is removed, and the given solution x=4 makes finding 'a' direct substitution. Slightly easier than average due to the structured guidance and elementary algebraic manipulation required. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02w Graph transformations: simple transformations of f(x) |
The function $f$ is defined by
$$f : x \mapsto |2x - a|, \quad x \in \mathbb{R},$$
where $a$ is a positive constant.
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = f(x)$, showing the coordinates of the points where the graph cuts the axes. [2]
\item On a separate diagram, sketch the graph of $y = f(2x)$, showing the coordinates of the points where the graph cuts the axes. [2]
\item Given that a solution of the equation $f(x) = \frac{1}{2}x$ is $x = 4$, find the two possible values of $a$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q7 [8]}}