document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=939777>Question 939777</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the curve y=3(1/2)^x<BR>\n" );
document.write( "Determine,\r<BR>\n" );
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document.write( "a) the horizontal asymptote<BR>\n" );
document.write( "b)the y-intercept<BR>\n" );
document.write( "c) the domain and range<BR>\n" );
document.write( "d)if its always increasing or decreasing </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #572710 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=572710\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the curve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%281%2F2%29%5Ex-1 ALIGN=MIDDLE  ALT=\"y=3%281%2F2%29%5Ex-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2F2%5Ex-1 ALIGN=MIDDLE  ALT=\"y=3%2F2%5Ex-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Determine,\r<BR>\n" );
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document.write( "a) \r<BR>\n" );
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document.write( "the horizontal asymptote is x-axis\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3Einfinity%2C+%283%2F2%5Ex%29-1+=-1+%29 ALIGN=MIDDLE  ALT=\"lim%28x-%3Einfinity%2C+%283%2F2%5Ex%29-1+=-1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3%2F2%5Ex-1 ALIGN=MIDDLE  ALT=\"y+=+3%2F2%5Ex-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is asymptotic to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-1 ALIGN=MIDDLE  ALT=\"y+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b)<BR>\n" );
document.write( "the y-intercept\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2F2%5Ex-1 ALIGN=MIDDLE  ALT=\"y=3%2F2%5Ex-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2F2%5E0-1 ALIGN=MIDDLE  ALT=\"y=3%2F2%5E0-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2F1-1 ALIGN=MIDDLE  ALT=\"y=3%2F1-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the y-intercept at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "c) <BR>\n" );
document.write( "the domain : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > all real numbers\r<BR>\n" );
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document.write( "the range:{ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E-1 ALIGN=MIDDLE  ALT=\"y%3E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > }  (all positive real numbers)\r<BR>\n" );
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document.write( "d)\r<BR>\n" );
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document.write( "if its always increasing or decreasing\r<BR>\n" );
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document.write( "it is always <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=decreasing ALIGN=MIDDLE  ALT=\"decreasing\"   DISABLED_style= \"max-width:90%; height:auto;\" > because the y-value decreases as the x-value increases\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-25%2C25%2C+-10%2C+10%2C-1%2C-1%2C+3%2F2%5Ex-1%2C3%2F2%5Ex-1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-25%2C25%2C+-10%2C+10%2C-1%2C-1%2C+3%2F2%5Ex-1%2C3%2F2%5Ex-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " </SPAN>\n" );
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