document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179841>Question 1179841</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the absolute value equation that has a vertical reflection, shrunk horizontally by 1/2, vertically translated 3 units up and horizontally translated 2 units left </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850166 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **Understanding Absolute Value Transformations**\r<BR>\n" );
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document.write( "The general form of an absolute value function is:\r<BR>\n" );
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document.write( "f(x) = a |b(x - h)| + k\r<BR>\n" );
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document.write( "where:\r<BR>\n" );
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document.write( "* **a:** Controls vertical reflection and stretch/shrink.<BR>\n" );
document.write( "    * If a is negative, there's a vertical reflection.<BR>\n" );
document.write( "    * |a| > 1: Vertical stretch<BR>\n" );
document.write( "    * 0 < |a| < 1: Vertical shrink<BR>\n" );
document.write( "* **b:** Controls horizontal reflection and stretch/shrink.<BR>\n" );
document.write( "    * If b is negative, there's a horizontal reflection.<BR>\n" );
document.write( "    * |b| > 1: Horizontal shrink<BR>\n" );
document.write( "    * 0 < |b| < 1: Horizontal stretch<BR>\n" );
document.write( "* **h:** Horizontal shift (left or right).<BR>\n" );
document.write( "    * (x - h): Shifts the graph h units to the right.<BR>\n" );
document.write( "    * (x + h): Shifts the graph h units to the left.<BR>\n" );
document.write( "* **k:** Vertical shift (up or down).<BR>\n" );
document.write( "    * +k: Shifts the graph k units up.<BR>\n" );
document.write( "    * -k: Shifts the graph k units down.\r<BR>\n" );
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document.write( "**Applying the Given Transformations**\r<BR>\n" );
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document.write( "1.  **Vertical Reflection:** a = -1<BR>\n" );
document.write( "2.  **Horizontal Shrink by 1/2:** b = 2<BR>\n" );
document.write( "3.  **Vertical Translation 3 Units Up:** k = 3<BR>\n" );
document.write( "4.  **Horizontal Translation 2 Units Left:** h = -2\r<BR>\n" );
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document.write( "**Substituting the Values**\r<BR>\n" );
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document.write( "f(x) = -1 |2(x - (-2))| + 3\r<BR>\n" );
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document.write( "**Simplified Equation**\r<BR>\n" );
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document.write( "f(x) = - |2(x + 2)| + 3<BR>\n" );
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