document.write( "Question 493814: find the domain and sketch the graph of the function:(4-x^2)/(2-x) \n" ); document.write( "
Algebra.Com's Answer #335458 by swincher4391(1107)\"\" \"About 
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Recall that the domain is all values of x that exist within the function.\r
\n" ); document.write( "\n" ); document.write( "Some things to look out for are: division by 0 and square root of a negative number.\r
\n" ); document.write( "\n" ); document.write( "Notice that when x =2, we are dividing by 0, so x=2 is definitely not in the domain.\r
\n" ); document.write( "\n" ); document.write( "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]. \r
\n" ); document.write( "\n" ); document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "(-2,0) (-1,1) (0,2) (1,3) \r
\n" ); document.write( "\n" ); document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "Hope that helps!\r
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