SPS SPS SM Pure 2024 February — Question 12

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2024
SessionFebruary
TopicModulus function

12.
  1. Sketch the graph with equation $$y = | 3 x - 2 a |$$ where \(a\) is a positive constant.
    State the coordinates of each point where the graph cuts or meets the coordinate axes.
  2. Solve, in terms of \(a\), the inequality $$| 3 x - 2 a | \leqslant x + a$$ Given that \(| 3 x - 2 a | \leqslant x + a\)
  3. find, in terms of \(a\), the range of possible values of \(\mathrm { g } ( x )\), where $$\mathrm { g } ( x ) = 5 a - \left| \frac { 1 } { 2 } a - x \right|$$