Transformation of specific function type

A question is this type if and only if it involves transformations of a specific named function (sin, cos, ln, exponential, reciprocal) and asks to describe, sketch, or find equations.

6 questions · Moderate -0.2

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Edexcel P1 2024 January Q7
9 marks Standard +0.8
  1. (a) Sketch the graph of the curve \(C\) with equation
$$y = \frac { 4 } { x - k }$$ where \(k\) is a positive constant.
Show on your sketch
  • the coordinates of any points where \(C\) cuts the coordinate axes
  • the equation of the vertical asymptote to \(C\)
Given that the straight line with equation \(y = 9 - x\) does not cross or touch \(C\) (b) find the range of values of \(k\).
OCR MEI C1 2008 January Q10
11 marks Moderate -0.8
10
  1. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{450c1c3a-9290-4afa-a051-112b60cf19c0-3_753_775_360_726} \captionsetup{labelformat=empty} \caption{Fig. 10}
    \end{figure} Fig. 10 shows a sketch of the graph of \(y = \frac { 1 } { x }\).
    Sketch the graph of \(y = \frac { 1 } { x - 2 }\), showing clearly the coordinates of any points where it crosses the axes.
  2. Find the value of \(x\) for which \(\frac { 1 } { x - 2 } = 5\).
  3. Find the \(x\)-coordinates of the points of intersection of the graphs of \(y = x\) and \(y = \frac { 1 } { x - 2 }\). Give your answers in the form \(a \pm \sqrt { b }\). Show the position of these points on your graph in part (i).
AQA C3 Q7
Standard +0.3
7
  1. The sketch shows the graph of \(y = \sin ^ { - 1 } x\). \includegraphics[max width=\textwidth, alt={}, center]{9aac4ee4-2435-4315-a87d-fe9fa8e15665-006_819_824_456_591} Write down the coordinates of the points \(P\) and \(Q\), the end-points of the graph.
  2. Sketch the graph of \(y = - \sin ^ { - 1 } ( x - 1 )\).
AQA C3 2006 January Q7
5 marks Standard +0.3
7
  1. The sketch shows the graph of \(y = \sin ^ { - 1 } x\). \includegraphics[max width=\textwidth, alt={}, center]{908f530c-076d-47b1-90dd-38dbfe44f898-05_835_834_447_587} Write down the coordinates of the points \(P\) and \(Q\), the end-points of the graph.
  2. Sketch the graph of \(y = - \sin ^ { - 1 } ( x - 1 )\).
CAIE P1 2018 November Q4
6 marks Moderate -0.8
Functions f and g are defined by $$f : x \mapsto 2 - 3\cos x \text{ for } 0 \leqslant x \leqslant 2\pi,$$ $$g : x \mapsto \frac{1}{2}x \text{ for } 0 \leqslant x \leqslant 2\pi.$$
  1. Solve the equation \(\text{fg}(x) = 1\). [3]
  2. Sketch the graph of \(y = \text{f}(x)\). [3]
WJEC Unit 1 2024 June Q11
4 marks Easy -1.3
  1. Sketch the graph of \(y = 3^x\). Clearly label the coordinates of the point where the graph crosses the \(y\)-axis. [2]
  2. On the same set of axes, sketch the graph of \(y = 3^{(x+1)}\), clearly labelling the coordinates of the point where the graph crosses the \(y\)-axis. [2]