Graphs and Transformations

mpx

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\section*{Topic assessment}
\section*{Do not use a graphical calculator for this test.}
  1. The diagram below shows the graph .
Sketch, on separate diagrams, each of the following graphs, showing the coordinates of the two change points and the -intercept, as shown on the diagram above.
(a)
(b)

2. Sketch the following graphs on separate diagrams.
(a)
(b)
3. Given that ,
(a) Find the equation of the curve, , obtained by translating the curve horizontally 1 unit in the negative direction.
(b) Find the equation of the curve, , obtained by stretching the curve parallel to the -axis with scale factor 2 .
4.
Express in the completed square form, . Hence describe the transformation that map onto .
5. (a) Sketch the graph .
(b) Hence sketch the graph of on a separate diagram. Show the coordinates of any points where the graph cuts the coordinate axes.
\section*{MEI AS Maths Graphs Assessment}
  1. (a) Given that , sketch the graphs of and on the same axes.
    (b) Use algebra to find the -coordinates of the points where the graphs intersect.
  2. (a) Sketch the graph of , where .
Show the coordinates of the points where the graph cuts the coordinate axes.
(b) Hence sketch the graph of , on a separate diagram, showing the coordinates of the points where the graph cuts the coordinate axes.
Find the equation of the graph in the form

drawing