document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153574>Question 1153574</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The graph of <BR>\n" );
document.write( "f(x) = -1/2 (1/6)exponent is x-7 \r<BR>\n" );
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document.write( " +9 is shifted left 7 units, stretched vertically by a factor of 6, reflected about the x-axis, and then shifted downward 9 units. What is the equation of the new function, g(x)?<BR>\n" );
document.write( "g(x) = <BR>\n" );
document.write( " State the y-intercept of <BR>\n" );
document.write( "g(x).\r<BR>\n" );
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document.write( "(x, y) = \r<BR>\n" );
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document.write( "  \r<BR>\n" );
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document.write( "State the domain and range of <BR>\n" );
document.write( "g(x).<BR>\n" );
document.write( " (Enter your answers using interval notation.)<BR>\n" );
document.write( "domain    			<BR>\n" );
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document.write( "range			<BR>\n" );
document.write( " \r<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 #775846 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=775846\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SHIFTS OF THE PARENT FUNCTION:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=a%2Ab%5Ex ALIGN=MIDDLE  ALT=\"+f%28x%29=a%2Ab%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "​​ <BR>\n" );
document.write( "For any constants  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the function \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f+%28x+%29=+a%2Ab+%5E%28x%2Bc%29%2Bd ALIGN=MIDDLE  ALT=\"+f+%28x+%29=+a%2Ab+%5E%28x%2Bc%29%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-is stretched vertically by a factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28a%29%3E1 ALIGN=MIDDLE  ALT=\"abs%28a%29%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "-is compressed vertically by a factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28a%29%3C1 ALIGN=MIDDLE  ALT=\"abs%28a%29%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "-has a y-intercept of   (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "​​ -shifts the parent function vertically <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > units, in the same direction of the sign of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+ ALIGN=MIDDLE  ALT=\"d+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-horizontally <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, in the opposite direction of the sign of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "-the y-intercept becomes  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+%5E+%28c+%2Bd%29 ALIGN=MIDDLE  ALT=\"+b+%5E+%28c+%2Bd%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "-the horizontal asymptote becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+d ALIGN=MIDDLE  ALT=\"y+=+d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-the range becomes (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( "-the domain, (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >), remains unchanged \r<BR>\n" );
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document.write( "in your case we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-%281%2F2%29+%281%2F6%29%5E%28+x-7%29+%2B9 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-%281%2F2%29+%281%2F6%29%5E%28+x-7%29+%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the equation of the new function, <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;\" >:\r<BR>\n" );
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document.write( "- is shifted left <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7+units ALIGN=MIDDLE  ALT=\"7+units\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+-%281%2F2%29+%281%2F6%29%5E%28+x-7%2B7%29+%2B9 ALIGN=MIDDLE  ALT=\"g%28x%29+=+-%281%2F2%29+%281%2F6%29%5E%28+x-7%2B7%29+%2B9\"   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=g%28x%29+=+-%281%2F2%29+%281%2F6%29%5Ex+%2B9 ALIGN=MIDDLE  ALT=\"g%28x%29+=+-%281%2F2%29+%281%2F6%29%5Ex+%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-stretched vertically by a factor of<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6 ALIGN=MIDDLE  ALT=\"+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+6%28-1%2F2%29+%281%2F6%29%5Ex+%2B9 ALIGN=MIDDLE  ALT=\"g%28x%29+=+6%28-1%2F2%29+%281%2F6%29%5Ex+%2B9\"   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=g%28x%29+=+-3%2A%281%2F6%29%5Ex+%2B9 ALIGN=MIDDLE  ALT=\"g%28x%29+=+-3%2A%281%2F6%29%5Ex+%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-reflected about 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, so we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=%28-1%29%2A%28+-3%29%2A%281%2F6%29%5Ex+%2B9 ALIGN=MIDDLE  ALT=\"g%28x%29+=%28-1%29%2A%28+-3%29%2A%281%2F6%29%5Ex+%2B9\"   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=g%28x%29+=+3%2A%281%2F6%29%5Ex+%2B9 ALIGN=MIDDLE  ALT=\"g%28x%29+=+3%2A%281%2F6%29%5Ex+%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and then shifted downward <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > units, so we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+3%2A%281%2F6%29%5E+x+%2B9-9 ALIGN=MIDDLE  ALT=\"g%28x%29+=+3%2A%281%2F6%29%5E+x+%2B9-9\"   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=g%28x%29+=+3%2A%281%2F6%29%5Ex+ ALIGN=MIDDLE  ALT=\"g%28x%29+=+3%2A%281%2F6%29%5Ex+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "State the y-intercept of <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;\" >.\r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >) =(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<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" );
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document.write( " the domain and range of <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;\" >:\r<BR>\n" );
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document.write( "the range becomes (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >) <BR>\n" );
document.write( "the domain, (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity+ ALIGN=MIDDLE  ALT=\"-infinity+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   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+15%2C+-10%2C+15%2C+-%281%2F2%29+%281%2F6%29%5E%28+x-7%29+%2B9%2C3%2A%281%2F6%29%5Ex%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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