document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181096>Question 1181096</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The graph has an equation in the form of f(x) = a(1/2)^b(x+2)+k. What is the actual equation?\r<BR>\n" );
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document.write( "Please view the graph at:<BR>\n" );
document.write( "https://docs.google.com/document/d/1Cl3HrcoR6jibNzxfDTIilS3imSplLY8nQUU0OpU9vLA/edit?usp=sharing </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #810916 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=810916\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "f(x) = a(1/2)^b(x+2)+k<br><BR>\n" );
document.write( "NOTE: To make the form of the function absolutely clear, the whole exponent \"b(x+2)\" should be in parentheses: f(x) = a(1/2)^(b(x+2))+k<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+a%281%2F2%29%5E%28b%28x%2B2%29%29%2Bk ALIGN=MIDDLE  ALT=\"f%28x%29+=+a%281%2F2%29%5E%28b%28x%2B2%29%29%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use the two given points and the horizontal asymptote to get three equations that can be solved to determine the constants a, b, and k.<br><BR>\n" );
document.write( "(1) horizontal asymptote:<BR>\n" );
document.write( "For large values of x, the decaying exponential goes to zero, making the function close to f(x)=k.  Since the asymptote is y=4, we have k=4.<br><BR>\n" );
document.write( "(2) f(-2) = 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29+=+a%281%2F2%29%5Eb%28-2%2B2%29%2B4 ALIGN=MIDDLE  ALT=\"f%28-2%29+=+a%281%2F2%29%5Eb%28-2%2B2%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+a%281%2F2%29%5E0%2B4 ALIGN=MIDDLE  ALT=\"1+=+a%281%2F2%29%5E0%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+a%2B4 ALIGN=MIDDLE  ALT=\"1+=+a%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-3 ALIGN=MIDDLE  ALT=\"a=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(3) f(-3) = -8:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29+=+-3%281%2F2%29%5Eb%28-3%2B2%29%2B4 ALIGN=MIDDLE  ALT=\"f%28-3%29+=+-3%281%2F2%29%5Eb%28-3%2B2%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8+=+-3%281%2F2%29%5Eb%28-1%29%2B4 ALIGN=MIDDLE  ALT=\"-8+=+-3%281%2F2%29%5Eb%28-1%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12+=+-3%282%5Eb%29 ALIGN=MIDDLE  ALT=\"-12+=+-3%282%5Eb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Eb=4 ALIGN=MIDDLE  ALT=\"2%5Eb=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "a=-3; b=2; k=4<br><BR>\n" );
document.write( "The function is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-3%281%2F2%29%5E%282%28x%2B2%29%29%2B4 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-3%281%2F2%29%5E%282%28x%2B2%29%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A graph:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-4%2C4%2C-6%2C6%2C-3%281%2F2%29%5E%282%28x%2B2%29%29%2B4%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-4%2C4%2C-6%2C6%2C-3%281%2F2%29%5E%282%28x%2B2%29%29%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );