document.write( "Question 1000359: Plz help me to explain the range of this equation. {f(x)=1÷x^2-2x-3} \n" ); document.write( "
Algebra.Com's Answer #617839 by solver91311(24713)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "I presume you mean \r
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\n" ); document.write( "\n" ); document.write( "It will be helpful to first factor the quadratic in the denominator so that you can find the zeros of the denominator and thereby know the boundaries of the region in which the denominator is negative and the regions where it is positive.\r
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\n" ); document.write( "\n" ); document.write( "The values that make the denominator zero are the vertical asymptotes of the graph. Since we know that the denominator is positive on one side of an value that makes the denominator zero and negative on the other side, we know that the function is going to take off toward either positive or negative infinity depending which side of the zero you are on.\r
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\n" ); document.write( "\n" ); document.write( "When becomes very large in either the positive or negative direction, the denominator will become very large, and, therefore, this function will get closer and closer to zero, but will never actually be zero. That gives us the positive part of the range -- the open interval 0 to infinity.\r
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\n" ); document.write( "\n" ); document.write( "The last question we have to answer is what is the highest value the function will reach when the denominator value is negative. For that, you need to find the value of the denominator at the vertex of the parabola represented by the denominator and then find the reciprocal of that value. Then the other half of your range will be the half-closed interval from negative infinity to the largest negative function value.\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it\r
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