document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160236>Question 1160236</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ls help me<BR>\n" );
document.write( "For the function<BR>\n" );
document.write( "f(x)=7/(8x+10)\r<BR>\n" );
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document.write( "find the range of by finding the values of a for which f(x)=a has a solution.<BR>\n" );
document.write( "Enter your answer as an inequality </SPAN>\n" );
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document.write( "The wording of the problem is faulty.<br><BR>\n" );
document.write( "The equation f(x)=a has a solution for all values of x except the single value that makes the denominator 0.  That value is x=-5/4.<br><BR>\n" );
document.write( "But determining that does NOT tell us the RANGE of the function; it only tells us the DOMAIN is all values except x=-5/4.<br><BR>\n" );
document.write( "To determine the range, we need to do some analysis.<br><BR>\n" );
document.write( "Note that the value of the function will never be 0, because the numerator is the constant 7.<br><BR>\n" );
document.write( "Arbitrarily large positive values of x will make the function value positive and arbitrarily small; arbitrarily large negative values of x will make the function value negative and arbitrarily small.  So the range of the function includes all numbers close to 0, but not 0 itself.<br><BR>\n" );
document.write( "The excluded value in the domain is x=-5/4.  For values greater than -5/4 and arbitrarily close to -5/4, the value of the function will be arbitrarily large; so there is no upper bound on the range of the function.  And for values less than -5/4 and arbitrarily close to -5/4, the value of the function will be arbitrarily \"large negative\"; so there is no lower bound on the range of the function.<br><BR>\n" );
document.write( "ANSWER: The range of the function is all real numbers except 0.<br><BR>\n" );
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