Edexcel C3 — Question 7

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
TopicModulus function

7. The function \(f\) is defined by $$f : x \wp \rightarrow | 2 x - a | , x \in \mathbb { R }$$ where \(a\) is a positive constant.
  1. Sketch the graph of \(y = \mathrm { f } ( x )\), showing the coordinates of the points where the graph cuts the axes.
  2. On a separate diagram, sketch the graph of \(y = \mathrm { f } ( 2 x )\), showing the coordinates of the points where the graph cuts the axes.
  3. Given that a solution of the equation \(\mathrm { f } ( x ) = \frac { 1 } { 2 } x\) is \(x = 4\), find the two possible values of \(a\).