document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=976010>Question 976010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I graph y=(3.4)abs((.7)(x-4))+1 step by step using absolute value transformation?\r<BR>\n" );
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document.write( "I understand that you should try to start with y=abs(x) <BR>\n" );
document.write( "and that +1 means that the graph will be shifted by 1 up<BR>\n" );
document.write( "and that -4 means that I will be shifting the graph to right by 4 units. <BR>\n" );
document.write( "The problem is that I am not sure how to shrink the graph horizonally and by what number. What do I do with 3.4 and .7?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #597696 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39625)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=597696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283.4%29abs%28%280.7%29%28x-4%29%29%2B1 ALIGN=MIDDLE  ALT=\"y=%283.4%29abs%28%280.7%29%28x-4%29%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Critical x value will be for the absolute value part to be 0.  That happens at x=4.  The graph has two branches.  For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C4 ALIGN=MIDDLE  ALT=\"x%3C4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=4 ALIGN=MIDDLE  ALT=\"x%3E=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=4 ALIGN=MIDDLE  ALT=\"x%3E=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, expression inside abs val is positive or zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3.4%28%280.7%29%28x-4%29%29%2B1 ALIGN=MIDDLE  ALT=\"y=3.4%28%280.7%29%28x-4%29%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3.4%280.7x-2.8%29%2B1 ALIGN=MIDDLE  ALT=\"y=3.4%280.7x-2.8%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2.38x-9.52%2B1 ALIGN=MIDDLE  ALT=\"y=2.38x-9.52%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2.38x-8.52 ALIGN=MIDDLE  ALT=\"y=2.38x-8.52\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----and you ONLY want the part where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=4 ALIGN=MIDDLE  ALT=\"x%3E=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >; NOTHING to the left.\r<BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C4 ALIGN=MIDDLE  ALT=\"x%3C4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, expression inside the abs val is NEGATIVE.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3.4%28%28-1%29%280.7%29%28x-4%29%29%2B1 ALIGN=MIDDLE  ALT=\"y=3.4%28%28-1%29%280.7%29%28x-4%29%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3.4%28-.7x%2B2.8%29%2B1 ALIGN=MIDDLE  ALT=\"y=3.4%28-.7x%2B2.8%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2.38x%2B9.52%2B1 ALIGN=MIDDLE  ALT=\"y=-2.38x%2B9.52%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2.38x%2B10.52 ALIGN=MIDDLE  ALT=\"y=-2.38x%2B10.52\"   DISABLED_style= \"max-width:90%; height:auto;\" >------and you ONLY want the part to the left of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >; nothing to the right.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-4%2C10%2C-2%2C12%2C%283.4%29abs%28%280.7%29%28x-4%29%29%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-4%2C10%2C-2%2C12%2C%283.4%29abs%28%280.7%29%28x-4%29%29%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "DISCUSSION OF TRANSFORMATION<BR>\n" );
document.write( "The equation and graph fundamentally starts from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=abs%28x%29 ALIGN=MIDDLE  ALT=\"y=abs%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This would be a \"V\" shaped figure, with the sharp corner at the origin, and both parts are above the x-axis, and therefore, y is non-negative everywhere.  Shift this 4 units to the right, and 1 unit up, and you are at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=abs%28x-4%29%2B1 ALIGN=MIDDLE  ALT=\"y=abs%28x-4%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Same shape, just shifted so the vertex is now at (4,1), the sharp point of the \"V\".<BR>\n" );
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document.write( "The factor,  0.7, squashes the graph vertically; and then the factor  3.4, stretches the graph vertically, MORE SO than the factor of the 0.7 did.  This combination of factors only affects the slope or slopes of each branch.  The combined factor for this is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.4%2A0.7=2.38 ALIGN=MIDDLE  ALT=\"3.4%2A0.7=2.38\"   DISABLED_style= \"max-width:90%; height:auto;\" >; overall, this stretches the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=abs%28x-4%29 ALIGN=MIDDLE  ALT=\"y=abs%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > vertically; but still same vertex or sharp point at  (4,1).  The factor is not arranged to affect the \"1\". </SPAN>\n" );
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