2Module 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"
3x = 0 y = 0, so the graph goes through the origin. The function is an example of a cubic function.To sketch the graph we notice the following:x = 0 y = 0, so the graph goes through the origin.xAs x increases, y increases quicklye.g. x = 1 y = 1;x = 2 y = 8The graph has 180 rotational symmetry about the originWhen sketching a graph, we try not to PLOT points. We want the general shape not an accurate drawing.e.g. x = -1 y = -1;x = -2 y = -8
4We have seen that the quadratic function is a translation of byIn a similar way, is a translation of
5is another cubic function Suppose we translate this function by
6is another cubic function The equation for the translation by isThe same rule works for all functions!
7x = 0 ( infinity ) x = 2 ; x = 3 e.g. (a) Sketch the graph of (b) Write down the translation of the graph by(c) Sketch the new graph.x = 0 ( infinity )Solution: (a)This means that on the graph, x can never be 0As x increases, y decreasesx = 2 ;x = 3 e.g. x = 1 y = 1;The graph has 180 rotational symmetry about the origin e.g.
8The graph ofAs x increases, y decreasesRotational symmetryOn this graph, the x-and y-axes form asymptotesAsymptotes are lines that a graph approaches as x or y approaches infinity.
14SUMMARYThe function given by translating any functionby the vector is given bySo, to find the translated function, wereplace by andadd( Notice that adding q is the same as replacing y by y – q. We’ll need this later. )
15ExerciseUsing the same axes for each pair, sketch the following functions:1.andand2.3.andCheck your answers using “Autograph” or a graphical calculator.
17The 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.
18The function is an example of a cubic function. The graph has 180 rotational symmetry about the origin.
20SUMMARYThe function given by translating any functionby the vector is given bySo, to find the translated function, wereplace by andadd( Notice that adding q is the same as replacing y by y – q. We’ll need this later. )
21The equation for the translation by is The same rule works for all functions!is another cubic functione.g.
22We usually show the asymptotes with a broken line. The equations of the asymptotes must always be givenThe graph of