document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=374505>Question 374505</A>: <I><SPAN STYLE=\"word-break: break-all;\"> List the transformations, in order, for the following function:<BR>\n" );
document.write( "f(x)=4-3^x-1\r<BR>\n" );
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document.write( "The first thing I did was rewrite the function: f(x)=-3^(x-1)+4\r<BR>\n" );
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document.write( "- Horizontally shifts 1 unit to the right (because of (x-1))<BR>\n" );
document.write( "- Reflects about the x-axis (because of the negative in front of the 3)<BR>\n" );
document.write( "- Vertically shifts 4 units up (because of the +4)\r<BR>\n" );
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document.write( "Is this correct?\r<BR>\n" );
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document.write( "Does the function vertically stretch by a factor of 3? \r<BR>\n" );
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document.write( "In my notes a compress/stretch is said to be: a > 1 then vertically stretches by factor of a<BR>\n" );
document.write( "0 < a < 1 vertically compresses by factor of a\r<BR>\n" );
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document.write( "But the instructor walked us through this problem but did not mention anything about a vertical stretch or compression. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266543 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3759)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=266543\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first thing I did was rewrite the function: f(x)=-3^(x-1)+4\r<BR>\n" );
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document.write( "- Horizontally shifts 1 unit to the right (because of (x-1))<BR>\n" );
document.write( "- Reflects about the x-axis (because of the negative in front of the 3)<BR>\n" );
document.write( "- Vertically shifts 4 units up (because of the +4)\r<BR>\n" );
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document.write( "Is this correct?<br><BR>\n" );
document.write( "Yes.<br><BR>\n" );
document.write( "Does the function vertically stretch by a factor of 3?<br><BR>\n" );
document.write( "No.<br><BR>\n" );
document.write( "In my notes a compress/stretch is said to be: a > 1 then vertically stretches by factor of a<BR>\n" );
document.write( "0 < a < 1 vertically compresses by factor of a<br><BR>\n" );
document.write( "This is all correct. However, your \"base\" function, from which the transformations are made, is<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;\" ><BR>\n" );
document.write( "The \"3\" is part of the base function. If you had<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29+=+-2%2A3%5E%28x-1%29+%2B+4 ALIGN=MIDDLE  ALT=\"h%28x%29+=+-2%2A3%5E%28x-1%29+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then the \"2\" would be the vertical stretch factor. Your f(x) does not have any vertical stretch factor (other than 1 (which is \"no stretch\")). </SPAN>\n" );
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