document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194666>Question 1194666</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. For the functions f(x) = 2^x and g(x) = 3^x :\r<BR>\n" );
document.write( "\n" );
document.write( "a) What are the Domains and Ranges of these functions?\r<BR>\n" );
document.write( "\n" );
document.write( "b) What point(s) do they have in common and why?\r<BR>\n" );
document.write( "\n" );
document.write( "c) Starting with y = 2^x, what would y = 2^x+4  -  3 look like in comparison to y = 2^x? \r<BR>\n" );
document.write( "\n" );
document.write( "d) How does y=(1/2)^x look in relation to y = 2^x? Why is this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826922 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=826922\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( " 1. For the functions \r<BR>\n" );
document.write( "\n" );
document.write( "<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 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+3%5Ex++ ALIGN=MIDDLE  ALT=\"g%28x%29+=+3%5Ex++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a) What are the Domains and Ranges of these functions?\r<BR>\n" );
document.write( "\n" );
document.write( "for <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;\" >:\r<BR>\n" );
document.write( "\n" );
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" );
document.write( "\n" );
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+0 ALIGN=MIDDLE  ALT=\"f%28x%29+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > } (all positive real numbers)\r<BR>\n" );
document.write( "\n" );
document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+3%5Ex++ ALIGN=MIDDLE  ALT=\"g%28x%29+=+3%5Ex++\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
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)<BR>\n" );
document.write( "range: { <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29 ALIGN=MIDDLE  ALT=\"g%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=g%28x%29+%3E+0 ALIGN=MIDDLE  ALT=\"g%28x%29+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > } (all positive real numbers)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b) What point(s) do they have in common and why?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "points where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+g%28x%29+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+g%28x%29+\"   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=2%5Ex=+3%5Ex+ ALIGN=MIDDLE  ALT=\"2%5Ex=+3%5Ex+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ........ since the bases are different, equation will be true only 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;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E0=+3%5E0 ALIGN=MIDDLE  ALT=\"2%5E0=+3%5E0\"   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=1=1 ALIGN=MIDDLE  ALT=\"1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "c) Starting with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%5Ex ALIGN=MIDDLE  ALT=\"y+=+2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >, what would <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%5E%28x%2B4%29+-+3 ALIGN=MIDDLE  ALT=\"y+=+2%5E%28x%2B4%29+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > look like in comparison to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%5Ex ALIGN=MIDDLE  ALT=\"y+=+2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
document.write( "\n" );
document.write( "Parent Function: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%5Ex ALIGN=MIDDLE  ALT=\"y+=+2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Horizontal Shift: Left ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > units<BR>\n" );
document.write( "Vertical Shift: Down , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > units\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%2C+2%5Ex%2C+2%5E%28x%2B4%29-3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2%5Ex%2C+2%5E%28x%2B4%29-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "d) How does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29%5Ex ALIGN=MIDDLE  ALT=\"y=%281%2F2%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > look in relation to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%5Ex ALIGN=MIDDLE  ALT=\"y+=+2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >? Why is this?\r<BR>\n" );
document.write( "\n" );
document.write( "these are inverse to each other\r<BR>\n" );
document.write( "\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5Ex+=1%2F2%5Ex ALIGN=MIDDLE  ALT=\"%281%2F2%29%5Ex+=1%2F2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> which is inverse to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex ALIGN=MIDDLE  ALT=\"2%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<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%2C+2%5Ex%2C+%281%2F2%29%5Ex%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2%5Ex%2C+%281%2F2%29%5Ex%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );