Sketch y=|linear| then solve equation or inequality (numeric coefficients)

Sketch the graph of y = |linear expression| with specific numeric coefficients, then solve a related equation or inequality, e.g. |2x-3| = x+4 or |2x-3| < 3x+2.

8 questions · Moderate -0.8

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CAIE P3 2020 March Q1
4 marks Moderate -0.8
1
  1. Sketch the graph of \(y = | x - 2 |\).
  2. Solve the inequality \(| x - 2 | < 3 x - 4\).
Edexcel C34 2015 January Q3
12 marks Moderate -0.3
3. The function \(g\) is defined by $$\mathrm { g } : x \mapsto | 8 - 2 x | , \quad x \in \mathbb { R } , \quad x \geqslant 0$$
  1. Sketch the graph with equation \(y = \mathrm { g } ( x )\), showing the coordinates of the points where the graph cuts or meets the axes.
  2. Solve the equation $$| 8 - 2 x | = x + 5$$ The function f is defined by $$\mathrm { f } : x \mapsto x ^ { 2 } - 3 x + 1 , \quad x \in \mathbb { R } , \quad 0 \leqslant x \leqslant 4$$
  3. Find fg(5).
  4. Find the range of f. You must make your method clear.
Edexcel C3 2010 June Q4
10 marks Moderate -0.8
4. The function \(f\) is defined by $$f : x \mapsto | 2 x - 5 | , \quad x \in \mathbb { R }$$
  1. Sketch the graph with equation \(y = \mathrm { f } ( x )\), showing the coordinates of the points where the graph cuts or meets the axes.
  2. Solve \(\mathrm { f } ( x ) = 15 + x\). The function \(g\) is defined by $$g : x \mapsto x ^ { 2 } - 4 x + 1 , \quad x \in \mathbb { R } , \quad 0 \leqslant x \leqslant 5$$
  3. Find fg(2).
  4. Find the range of g.
CAIE P3 2020 Specimen Q3
4 marks Easy -1.3
3
  1. Sketch the graph of \(y = | 2 x - 3 |\).
  2. Solve the inequality \(3 x - 1 > | 2 x - 3 |\).
OCR MEI Paper 2 2021 November Q4
3 marks Easy -1.8
4 Sketch the graph of \(y = | 2 x - 3 |\).
AQA C3 2007 January Q7
9 marks Moderate -0.3
7
  1. Sketch the graph of \(y = | 2 x |\).
  2. On a separate diagram, sketch the graph of \(y = 4 - | 2 x |\), indicating the coordinates of the points where the graph crosses the coordinate axes.
  3. Solve \(4 - | 2 x | = x\).
  4. Hence, or otherwise, solve the inequality \(4 - | 2 x | > x\).
AQA C3 2015 June Q2
13 marks Moderate -0.3
2
  1. Sketch, on the axes below, the curve with equation \(y = 4 - | 2 x + 1 |\), indicating the coordinates where the curve crosses the axes.
  2. Solve the equation \(x = 4 - | 2 x + 1 |\).
  3. Solve the inequality \(x < 4 - | 2 x + 1 |\).
  4. Describe a sequence of two geometrical transformations that maps the graph of \(y = | 2 x + 1 |\) onto the graph of \(y = 4 - | 2 x + 1 |\).
    [0pt] [4 marks] \section*{Answer space for question 2}
    1. \includegraphics[max width=\textwidth, alt={}, center]{2df59047-3bfe-4b9c-a77f-142bc7506cbc-04_851_1459_1000_319}
OCR MEI C3 Q3
6 marks Moderate -0.8
  1. Sketch the graph of \(y = |3x - 6|\). [2]
  2. Solve the equation \(|3x - 6| = x + 4\) and illustrate your answer on your graph. [4]