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1.You need to identify what type of function the picture is representing 2.From the graph it is obvious that the graph is an absolute value graph because it llooks|dw:1436099455742:dw| 3.You should know that an absolute value graph of IxI look like |dw:1436099603734:dw| The graph in the picture however is a horizontal translation and vertical translation of IxI as it doesnt start at the origin The number within the absolute value sign(with the x) indicates whether it moves to the left to the left or the right,it also gives an indication on the number it moves to E.g. y=Ix-2I would translate(move the graph) to +2 on the x axis|dw:1436100092588:dw| y=Ix+2I would translate*(move the praph) it to -2 on the x axis |dw:1436100148470:dw| Negative =moves to the right Positive=Moves to the left The number outside the absolute value sign indicates whether the graph moves up or down E.g.IxI+1 would move the graph up 1|dw:1436100321483:dw| IxI-1 would move the graph down 1to -1|dw:1436100385437:dw| Positive moves up Negative Moves down With this mind by looking at the graph we can put the first part of the inequality ,the equation 1.If you look at the picture can you see that it moved to the left to -2 Therefore thethe 1st part of the equation isy= Ix+2I 2.If you look at the picture you an also see that the bottom of the graph moved down to -3 So adding on to the second part of the equation the equation should be y= Ix+2I-3 because it moved to the left(2) and moved down(3) The Inequality Now you got the equation y= Ix+2I-3 you need to replace the = sign with an inequality sign .If you look on the graph the lines surrounding the graph is dotted----------- This means the inequality is either going to be <>greater than or less than .If it was a solid line it you would use the grreater /less thann signs but with a line under neath them|dw:1436100982865:dw| which mean than it is greater/less than but equal to Now you have to figure outwhich sign do you need to use .To do this you have to choose a point on the graph and substtitue into the inequalty.Usually you should test the point (0,0) however you can see that it is within the graph.So you need to use a coordinate outside the graph.Lets use (3,1) All you need to do is substitute 3 and 1 into the equation for Y and x So the equation is y=Ix+2I-3 Replace the = sign with an inequality sign Lets use < y>Ix+2I-3 Substitute (3,1) 3>1+2-3 3>0 Think to yourself is 0 greater than -1 This is true.Therefore the inequality is y>Ix+2I-3 Things to Remember 1.Identify the graph 2.Identify any horzontal or vertical translations 3.Replace the = sign withan inequality and test out a point that is not in the graph to prove the inequality