document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139317>Question 1139317</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following is a transformation applied to the base function f(x)=-1\5(10^x+7)+12?\r<BR>\n" );
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document.write( "A horizontal translation 12 to the right <BR>\n" );
document.write( "A reflection in the y -axis <BR>\n" );
document.write( "A horizontal stretch by a factor of 5 <BR>\n" );
document.write( "A vertical compression by a factor of 1/5  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #759879 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13215)</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=759879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) The function you show is not the base function; it is a transformed function.<br><BR>\n" );
document.write( "(2) The function as you show it is this: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%5C5%2810%5Ex%2B7%29%2B12 ALIGN=MIDDLE  ALT=\"-1%5C5%2810%5Ex%2B7%29%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The backslash (\"\\") is not used to represent division (fractions); the program on this web site that interprets expressions simply ignores the backslash, creating the coefficient \"-15\".  Using the correct symbol for representing fractions, your transformed function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F5%2810%5Ex%2B7%29%2B12 ALIGN=MIDDLE  ALT=\"-1%2F5%2810%5Ex%2B7%29%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That clearly is not what you want; the entire coefficient \"-1/5\" must be in parentheses: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F5%29%2810%5Ex%2B7%29%2B12 ALIGN=MIDDLE  ALT=\"%28-1%2F5%29%2810%5Ex%2B7%29%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Finally, it is highly probable that, in the transformed function, the \"+7\" is supposed to be part of the exponent; so you need to put the entire exponent in parentheses: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F5%29%2810%5E%28x%2B7%29%29%2B12 ALIGN=MIDDLE  ALT=\"%28-1%2F5%29%2810%5E%28x%2B7%29%29%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the base function is apparently <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5Ex ALIGN=MIDDLE  ALT=\"10%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Let's look now at the transformations that are made to this base function, in the order that they are made (as determined by standard order of operations).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E%28x%2B7%29 ALIGN=MIDDLE  ALT=\"10%5E%28x%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (replace x with x+7) represents a horizontal shift of 7 to the left.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F5%2910%5E%28x%2B7%29 ALIGN=MIDDLE  ALT=\"%28-1%2F5%2910%5E%28x%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (add the coefficient (-1/5)) represents a reflection in the x-axis and a vertical compression by a factor of 1/5.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F5%29%2810%5Ex%2B7%29%2B12 ALIGN=MIDDLE  ALT=\"%28-1%2F5%29%2810%5Ex%2B7%29%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > (adding the \"+12\" at the end) represents a vertical shift of +12.<BR>\n" );
document.write( "There is no horizontal stretch or compression; that would be indicated by something like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E%283x%29 ALIGN=MIDDLE  ALT=\"10%5E%283x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Only one of those transformations is one of the answer choices. </SPAN>\n" );
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