document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=933404>Question 933404</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help!<BR>\n" );
document.write( "The graph of function h is created by shifting the graph of y=2^x to the left 3 units, then reflecting it in the x-axis, and finally shifting it up 8 units. Find h(x)\r<BR>\n" );
document.write( "\n" );
document.write( "I think it's something on the order of: 2(x+3)+8 not sure about the 2. Unsure how to solve </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #566782 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=566782\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When we have an exponential equation of the form y=a^x ± k, then the graph will be moved up or down k units.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When we make a change in the exponent of the equation, a left or right shift happens. In general, for an exponential equation of the form y=a^(x±c) the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%5Ex ALIGN=MIDDLE  ALT=\"y=a%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be moved left <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > units if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive, and right <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > units if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative.\r<BR>\n" );
document.write( "\n" );
document.write( "If a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=negative ALIGN=MIDDLE  ALT=\"negative\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sign ALIGN=MIDDLE  ALT=\"sign\"   DISABLED_style= \"max-width:90%; height:auto;\" > is placed in front of an exponential function, then it will be reflected over the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-axis ALIGN=MIDDLE  ALT=\"x-axis\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "The graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-a%5Ex ALIGN=MIDDLE  ALT=\"y+=+-a%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be obtained by reflecting the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%5Ex ALIGN=MIDDLE  ALT=\"y+=+a%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the x-axis.\r<BR>\n" );
document.write( "\n" );
document.write( "The graph of the exponential equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%5E%28-x%29 ALIGN=MIDDLE  ALT=\"y+=+a%5E%28-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be obtained by reflecting the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%5Ex ALIGN=MIDDLE  ALT=\"y+=+a%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-axis%7D%7D.%0D%0A%0D%0A%0D%0A%0D%0Ato+translated+left+%7B%7B%7B3 ALIGN=MIDDLE  ALT=\"y-axis%7D%7D.%0D%0A%0D%0A%0D%0A%0D%0Ato+translated+left+%7B%7B%7B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > units means subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%5E%28x-3%29 ALIGN=MIDDLE  ALT=\"y=2%5E%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "to reflect about the x-axis place a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=negative ALIGN=MIDDLE  ALT=\"negative\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sign ALIGN=MIDDLE  ALT=\"sign\"   DISABLED_style= \"max-width:90%; height:auto;\" > in front\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%5E%28x-3%29 ALIGN=MIDDLE  ALT=\"y=-2%5E%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "to shifting it up <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > units means add  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%5E%28x-3%29%2B8 ALIGN=MIDDLE  ALT=\"y=-2%5E%28x-3%29%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
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%2C2%5Ex%2C+-2%5E%28x%2B3%29%2B8%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C2%5Ex%2C+-2%5E%28x%2B3%29%2B8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );