Sketch |f(x)| only

Questions that only require sketching y = |f(x)| without solving any inequality involving a constant k.

2 questions · Standard +0.6

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CAIE Further Paper 1 2020 November Q6
12 marks Standard +0.8
6 The curve \(C\) has equation \(\mathrm { y } = \frac { \mathrm { x } ^ { 2 } + \mathrm { x } - 1 } { \mathrm { x } - 1 }\).
  1. Find the equations of the asymptotes of \(C\).
  2. Show that there is no point on \(C\) for which \(1 < y < 5\).
  3. Find the coordinates of the intersections of \(C\) with the axes, and sketch \(C\).
  4. Sketch the curve with equation \(\mathrm { y } = \left| \frac { \mathrm { x } ^ { 2 } + \mathrm { x } - 1 } { \mathrm { x } - 1 } \right|\).
Edexcel C34 2015 June Q3
10 marks Standard +0.3
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4c08fbab-283e-4c92-89a4-10f68f37e133-05_799_885_118_534} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x )\), where $$\mathrm { f } ( x ) = ( 2 x - 5 ) \mathrm { e } ^ { x } , \quad x \in \mathbb { R }$$ The curve has a minimum turning point at \(A\).
  1. Use calculus to find the exact coordinates of \(A\). Given that the equation \(\mathrm { f } ( x ) = k\), where \(k\) is a constant, has exactly two roots,
  2. state the range of possible values of \(k\).
  3. Sketch the curve with equation \(y = | \mathrm { f } ( x ) |\). Indicate clearly on your sketch the coordinates of the points at which the curve crosses or meets the axes.