Sketch y=|f(x)| for non-linear f(x)

Sketch the graph of y = |f(x)| where f(x) is non-linear (e.g. quadratic, exponential, logarithmic), showing axis intercepts and key features.

4 questions · Moderate -0.7

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Edexcel C3 2010 January Q5
3 marks Moderate -0.3
5. Sketch the graph of \(y = \ln | x |\), stating the coordinates of any points of intersection with the axes.
Edexcel C3 2015 June Q2
10 marks Moderate -0.8
2. Given that $$\mathrm { f } ( x ) = 2 \mathrm { e } ^ { x } - 5 , \quad x \in \mathbb { R }$$
  1. sketch, on separate diagrams, the curve with equation
    1. \(y = \mathrm { f } ( x )\)
    2. \(y = | \mathrm { f } ( x ) |\) On each diagram, show the coordinates of each point at which the curve meets or cuts the axes. On each diagram state the equation of the asymptote.
  2. Deduce the set of values of \(x\) for which \(\mathrm { f } ( x ) = | \mathrm { f } ( x ) |\)
  3. Find the exact solutions of the equation \(| \mathrm { f } ( x ) | = 2\)
OCR C3 Q4
9 marks Moderate -0.3
4. The function f is defined by $$\mathrm { f } ( x ) \equiv x ^ { 2 } - 2 a x , \quad x \in \mathbb { R }$$ where \(a\) is a positive constant.
  1. Showing the coordinates of any points where the graph meets the axes, sketch the graph of \(y = | \mathrm { f } ( x ) |\). The function \(g\) is defined by $$\mathrm { g } ( x ) \equiv 3 a x , \quad x \in \mathbb { R } .$$
  2. Find \(\mathrm { fg } ( \mathrm { a } )\) in terms of \(a\).
  3. Solve the equation $$\operatorname { gf } ( x ) = 9 a ^ { 3 }$$
Pre-U Pre-U 9794/2 2015 June Q3
4 marks Easy -1.2
3 The function f is given by \(\mathrm { f } ( x ) = | x - 2 | + 3\) for \(- 5 \leqslant x \leqslant 5\).
  1. Sketch the graph of \(y = \mathrm { f } ( x )\).
  2. Explain why f is not one-one.