deswa1
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- Jul 12, 2011
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First off, you want to graph y=(x-4)/(x+2). There are a few ways to do this. Personally, I would realise that there is no value at x=-2 because the denominator becomes zero. At this point approaching from the negative side, y approaches infinity and approaching from the positive side, y approaches negative infinity. Also, as x approaches plus or minus infinity, y approaches one which is a horizontal asymptote. Finally, When y=0, x=4 which is the x intercept and when x=0, y=-2 which is the y intercept. Use this information (plus the general shape of the hyperbola) to graph it. Then simply test values 'inside' and 'outside' the hyperbola to work out what areas satisfy the inequality.
Another way to graph the function is as follows:
y=(x-4)/(x+2)=(x+2-6)/(x+2)
y=1-(6/x+2)
NOTE: If all you wanted to do was solve the inequality, it would be much easier to do it algebriacally (all less than signs should be less than or equal to):
(x-4)/(x+2)>0
(x-4)(x+2)>0 on multiplying by (x+2)^2
x>4, x<-2
Another way to graph the function is as follows:
y=(x-4)/(x+2)=(x+2-6)/(x+2)
y=1-(6/x+2)
NOTE: If all you wanted to do was solve the inequality, it would be much easier to do it algebriacally (all less than signs should be less than or equal to):
(x-4)/(x+2)>0
(x-4)(x+2)>0 on multiplying by (x+2)^2
x>4, x<-2
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