document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=987496>Question 987496</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the function f(x) = 6-(1/x+3), answer the following questions:<BR>\n" );
document.write( "A) Domain and range<BR>\n" );
document.write( "B) 1 to 1 or not<BR>\n" );
document.write( "C) Continuous or not (if continuous tell where)<BR>\n" );
document.write( "D) Increasing, decreasing, both (if both tell where), or neither<BR>\n" );
document.write( "E) Bounded above, bounded below, bounded, or unbounded (if unbounded, tell where)<BR>\n" );
document.write( "F) Roots </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #608254 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=608254\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am going to write this as 6- [1/(x+3)]<BR>\n" );
document.write( "That is very different from 6-(1/x) +3<BR>\n" );
document.write( "The domain is all reals except x= -3<BR>\n" );
document.write( "Range: look at x approaching -3 from the + side and from the - side.<BR>\n" );
document.write( "As x approaches from the + side, the fraction gets large positive 1/(-2.999+3)=1/.001=1000, and that makes the function large negative, since it is being subtracted.<BR>\n" );
document.write( ";<BR>\n" );
document.write( "And by the same approach from the negative side, it can be infinite negative as well, which subtracted, makes the range infinitely positive.<BR>\n" );
document.write( "It is DISCONTINUOUS at x=-3<BR>\n" );
document.write( "It increases from minus infinity to 6 and decreases from positive infinity to 6 as x gets large negative.  The bounds are asymptote is 6. As x gets large positive, the function goes from negative infinity to 6.<BR>\n" );
document.write( "It is 1 to 1, for while it doesn't look like it passes either horizontal or vertical line test, the function does change slightly.<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Solving for roots, -1/(x+3)=-6<BR>\n" );
document.write( "6x+18=1<BR>\n" );
document.write( "6x=-17<BR>\n" );
document.write( "x= -(17/6)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-20%2C20%2C-50%2C50%2C6-%281%2F%28x%2B3%29%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-20%2C20%2C-50%2C50%2C6-%281%2F%28x%2B3%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );