Single transformation sketch

Questions asking to sketch a single transformation of f(x) such as f(x+a), f(ax), af(x), or |f(x)|, showing key features like intercepts and turning points.

4 questions

AQA C3 2013 June Q6
6
  1. Sketch the graph of \(y = \cos ^ { - 1 } x\), where \(y\) is in radians. State the coordinates of the end points of the graph.
  2. Sketch the graph of \(y = \pi - \cos ^ { - 1 } x\), where \(y\) is in radians. State the coordinates of the end points of the graph.
    (2 marks)
    \includegraphics[max width=\textwidth, alt={}, center]{063bbfa5-df49-44a1-8143-5e076397f63f-05_759_1258_678_431}
    \includegraphics[max width=\textwidth, alt={}, center]{063bbfa5-df49-44a1-8143-5e076397f63f-05_751_1241_1564_443}
OCR MEI C1 Q6
  1. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{9106e6b2-0b36-4ebf-ace3-a30570df73d3-2_754_780_317_763} \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).
OCR AS Pure 2017 Specimen Q1
1
  1. The diagram below shows the graph of \(y = \mathrm { f } ( x )\).
    \includegraphics[max width=\textwidth, alt={}, center]{54bdddcb-c1ef-4b60-af6c-ac944cae29fe-03_793_1470_571_356}
    1. On the diagram in the Printed Answer Booklet draw the graph of \(y = \mathrm { f } ( x + 3 )\).
    2. Describe fully the transformation which transforms the graph of \(y = \mathrm { f } ( x )\) to the graph of \(y = - \mathrm { f } ( x )\).
  2. The point \(( 2,3 )\) lies on the graph of \(y = \mathrm { g } ( x )\). State the coordinates of its image when \(y = \mathrm { g } ( x )\) is transformed to
    1. \(\quad y = 4 \mathrm {~g} ( x )\)
    2. \(\quad y = \mathrm { g } ( 4 x )\).
OCR Pure 1 2017 Specimen Q3
3 The diagram below shows the graph of \(y = \mathrm { f } ( x )\).
\includegraphics[max width=\textwidth, alt={}, center]{2c30c315-c666-47d6-b05e-da71cb4decdd-05_755_1398_388_326}
  1. On the diagram in the Printed Answer Booklet, draw the graph of \(y = \mathrm { f } \left( \frac { 1 } { 2 } x \right)\).
  2. On the diagram in the Printed Answer Booklet, draw the graph of \(y = \mathrm { f } ( x - 2 ) + 1\).