document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129812>Question 1129812</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a. Describe the transformation that have been applied to the graph of F(x)=2^x to obtain the graph f(x)2^(x+1)-3\r<BR>\n" );
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document.write( "b. what is the Domain & Ranger of f(x)=2^(x+1)-3?\r<BR>\n" );
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document.write( "c. what is the equation of the asymptote for the graph of f(x)=2^(x+1)-3?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #746463 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=746463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  a.<BR>\n" );
document.write( "to describe the transformation that have been applied to given exponential function, recall: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%2Ab%5E%28x-h%29%2Bv ALIGN=MIDDLE  ALT=\"y=a%2Ab%5E%28x-h%29%2Bv\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the vertical transformation, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the horizontal shift, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v+ ALIGN=MIDDLE  ALT=\"v+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is the vertical shift\r<BR>\n" );
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document.write( "if given the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29=2%5Ex+ ALIGN=MIDDLE  ALT=\"F%28x%29=2%5Ex+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and obtain the graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%5E%28x%2B1%29-3 ALIGN=MIDDLE  ALT=\"f%28x%29=2%5E%28x%2B1%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "based on this equation, you see that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-1 ALIGN=MIDDLE  ALT=\"h+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and it means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29 ALIGN=MIDDLE  ALT=\"F%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > has been shifted <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=one+ ALIGN=MIDDLE  ALT=\"one+\"   DISABLED_style= \"max-width:90%; height:auto;\" >unit to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=left+ ALIGN=MIDDLE  ALT=\"left+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v+=+-3 ALIGN=MIDDLE  ALT=\"v+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29+ ALIGN=MIDDLE  ALT=\"F%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >has been shifted <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=three ALIGN=MIDDLE  ALT=\"three\"   DISABLED_style= \"max-width:90%; height:auto;\" > units <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=down ALIGN=MIDDLE  ALT=\"down\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. <BR>\n" );
document.write( "what is the Domain & Ranger of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%5E%28x%2B1%29-3 ALIGN=MIDDLE  ALT=\"f%28x%29=2%5E%28x%2B1%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >? \r<BR>\n" );
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document.write( "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( "Range:   { <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   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=f%28x%29+%3E+-3 ALIGN=MIDDLE  ALT=\"f%28x%29+%3E+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
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document.write( "c. what is the equation of the asymptote for the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%5E%28x%2B1%29-3 ALIGN=MIDDLE  ALT=\"f%28x%29=2%5E%28x%2B1%29-3\"   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=lim%28x-%3E-infinity%29 ALIGN=MIDDLE  ALT=\"lim%28x-%3E-infinity%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282%5E%28x+%2B+1%29+-+3%29+=+-3 ALIGN=MIDDLE  ALT=\"+%282%5E%28x+%2B+1%29+-+3%29+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Horizontal asymptote: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3 ALIGN=MIDDLE  ALT=\"y=-3\"   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=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2%5Ex%2C+2%5E%28x%2B1%29-3%2C-3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2%5Ex%2C+2%5E%28x%2B1%29-3%2C-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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