document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=926129>Question 926129</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Give the equation for a logarithmic function with base 4 that has been translated right 1 and up 5 and reflected over the x axis. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #562059 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=562059\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The logarithmic function, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%28b%2Cx%29 ALIGN=MIDDLE  ALT=\"y+=+log%28b%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , can be shifted <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > units vertically and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > units horizontally with the equation \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%28b%2C%28x%2Bh%29%29%2Bk ALIGN=MIDDLE  ALT=\"y+=+log%28b%2C%28x%2Bh%29%29%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( "Vertical shift\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3E+0 ALIGN=MIDDLE  ALT=\"k%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the graph would be shifted <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > units <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=up ALIGN=MIDDLE  ALT=\"up\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+%3C+0 ALIGN=MIDDLE  ALT=\"k+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the graph would be shifted <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   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( "Horizontal Shift\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+%3E+0 ALIGN=MIDDLE  ALT=\"h+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the graph would be shifted <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > units <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( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+%3C0 ALIGN=MIDDLE  ALT=\"h+%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the graph would be shifted <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > units <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=right ALIGN=MIDDLE  ALT=\"right\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Whenever the minus sign (-) is in front of the function notation, it indicates a reflection across the x-axis. For example, the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-f%28x%29%29 ALIGN=MIDDLE  ALT=\"%28-f%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a reflection of the graph of <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;\" > across the x-axis. \r<BR>\n" );
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document.write( "The graph of 3 -g(x) involves the reflection of the graph of g(x) across the x-axis and the upward shift of the reflected graph 3 units. \r<BR>\n" );
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document.write( "you are given:\r<BR>\n" );
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document.write( "a logarithmic function with base <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4 ALIGN=MIDDLE  ALT=\"b=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > that has been translated right <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 up <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=5 ALIGN=MIDDLE  ALT=\"k=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and reflected over the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > axis\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-log%284%2C%28x%2B1%29%29%2B5 ALIGN=MIDDLE  ALT=\"y+=+-log%284%2C%28x%2B1%29%29%2B5\"   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%2Clog%284%2Cx%29%2C-log%284%2C%28x%2B1%29%29%2B5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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