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7: More Graphs and Translations © Christine Crisp “Teach A Level Maths” Vol. 1: AS Core Modules.

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Presentation on theme: "7: More Graphs and Translations © Christine Crisp “Teach A Level Maths” Vol. 1: AS Core Modules."— Presentation transcript:

1 7: More Graphs and Translations © Christine Crisp “Teach A Level Maths” Vol. 1: AS Core Modules

2 More Graphs and Translations Module C1 "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

3 More Graphs and Translations When sketching a graph, we try not to PLOT points. We want the general shape not an accurate drawing. x  The function is an example of a cubic function. x = 0  y = 0, so the graph goes through the origin. As x increases, y increases quickly e.g. x = 1  y = 1; x = 2  y = 8 To sketch the graph we notice the following: The graph has 180  rotational symmetry about the origin e.g. x = - 1  y = - 1; x = - 2  y = - 8

4 More Graphs and Translations  In a similar way, is a translation of We have seen that the quadratic function is a translation of by

5 More Graphs and Translations is another cubic functionSuppose we translate this function by

6 More Graphs and Translations The same rule works for all functions! is another cubic functionThe equation for the translation by is

7 More Graphs and Translations This means that on the graph, x can never be 0 e.g. (a) Sketch the graph of (b) Write down the translation of the graph by (c) Sketch the new graph. Solution: (a) The graph has 180  rotational symmetry about the origin e.g. x = 0  ( infinity ) As x increases, y decreases e.g. x = 1  y = 1; x = 2  ; x = 3 

8 More Graphs and Translations As x increases, y decreases The graph of On this graph, the x -and y -axes form asymptotes Asymptotes are lines that a graph approaches as x or y approaches infinity. Rotational symmetry

9 More Graphs and Translations For the graph of As

10 More Graphs and Translations As For the graph of

11 More Graphs and Translations We usually show the asymptotes with a broken line. The equations of the asymptotes must always be given For the graph of

12 More Graphs and Translations (b)Translating by gives The asymptotes have also been translated

13 More Graphs and Translations So the graph of is

14 More Graphs and Translations SUMMARY The function given by translating any function by the vector is given by So, to find the translated function, we  replace by and  add ( Notice that adding q is the same as replacing y by y – q. We’ll need this later. )

15 More Graphs and Translations Using the same axes for each pair, sketch the following functions: Exercise 1.and 2. and 3.and Check your answers using “Autograph” or a graphical calculator.

16 More Graphs and Translations

17 The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied. For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

18 More Graphs and Translations The function is an example of a cubic function. The graph has 180  rotational symmetry about the origin.

19 More Graphs and Translations e.g. is a translation of of Translations

20 More Graphs and Translations SUMMARY The function given by translating any function by the vector is given by So, to find the translated function, we  replace by and  add ( Notice that adding q is the same as replacing y by y – q. We’ll need this later. )

21 More Graphs and Translations The equation for the translation by is The same rule works for all functions! is another cubic function e.g.

22 More Graphs and Translations We usually show the asymptotes with a broken line. The equations of the asymptotes must always be given The graph of

23 More Graphs and Translations The graph of is


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