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Question 493814: find the domain and sketch the graph of the function:(4-x^2)/(2-x)
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! Recall that the domain is all values of x that exist within the function.
Some things to look out for are: division by 0 and square root of a negative number.
Notice that when x =2, we are dividing by 0, so x=2 is definitely not in the domain.
It seems all other values work. So depending on your preference, the answer is (-oo,2) u (2,oo) [interval notation] or ([all reals | x =/ 2) [set builder notation].
As far as the graph goes, start plugging in values of x such as -2,-1,0,1,3 and see what range values pop-up. Then plot them on your graph.
(-2,0) (-1,1) (0,2) (1,3)
An easier way, if you are clever, is factor the numerator into (2-x)(2+x) and then cancel out the (2-x)s, you are left with 2+x. Surely you know how to graph that. But if not, remember your slope-intercept form where m=1 and b=2. Just remember to exclude x=2 since it does not exist within the domain.
Hope that helps!
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