document.write( "Question 713997: Find the domain and range of the function:\r
\n" ); document.write( "\n" ); document.write( "g(x) = 9/(x-1)\r
\n" ); document.write( "\n" ); document.write( "I need help determining the range. I understand that domain contains all real numbers but 1. \n" ); document.write( "

Algebra.Com's Answer #438638 by josgarithmetic(39630) $\"\"$ $\"About$

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You want to find the set of values that g(x) can be. You are not interested in what is g(x) at x=1, since g(x) has no meaning there. The meaningful ideas come from what happens NEAR x=1 to the left and to the right of x=1; and what happens as x goes unbounded toward negative and to positive infinities. \r
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\n" ); document.write( "\n" ); document.write( "Near x=1 on the left, g is negative and decreases without bound as x moves toward 1. As x goes further and further to the left, g begins to approach 0, but still g<0.\r
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\n" ); document.write( "\n" ); document.write( "Near x=1 on the right, g is now positive and increases upward without bound as x approaches 1, but as x goes to the right further and further, g moves toward 0 but g>0. \r
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\n" ); document.write( "\n" ); document.write( "Put the two together and g takes on all real numbers from negative infinity to positive infinity. \n" ); document.write( "

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