document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131579>Question 1131579</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I transform the equation y=&#8730;x to shift left 4 units, down 3 units, and reflect over the x-axis?\r<BR>\n" );
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document.write( "I tried to do this and got f(x)= -&#8730;(x+4) -3 but the answer key I have says it is f(x)=&#8730;(4-x) -3. Can you explain what I did wrong? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #748271 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=748271\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if they wanted a reflection about the x-axis, then your answer is partially correct.\r<BR>\n" );
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document.write( "if they wanted a reflection about the y-axis, then their answer is correct.\r<BR>\n" );
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document.write( "the order of the transformations is important.\r<BR>\n" );
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document.write( "if they want you to shift to the left, then shift down, then reflect, you have to do the transformations in that order.\r<BR>\n" );
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document.write( "taking what you described as what they wanted, then the program statement is:\r<BR>\n" );
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document.write( "transform the equation y = sqrt(x) to shift left 4 units, down 3 units, and reflect over the x-axis.\r<BR>\n" );
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document.write( "the answer would be:\r<BR>\n" );
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document.write( "y = sqrt(x) becomes y = -(sqrt(x + 4) - 3).\r<BR>\n" );
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document.write( "this is the same as y = -sqrt(x + 4) + 3.\r<BR>\n" );
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document.write( "your answer was y = -sqrt(x + 4) - 3, which would be incorrect, because the downward shift of 3 units had to be reflected as well.\r<BR>\n" );
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document.write( "if the problem statement was:\r<BR>\n" );
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document.write( "transform the equation y = sqrt(x) to shift left 4 units, down 3 units, and reflect over the y-axis.\r<BR>\n" );
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document.write( "then the answer would be:\r<BR>\n" );
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document.write( "y = sqrt(x) becomes y = sqrt(-x + 4) - 3 which becomes y = sqrt(4-x) - 3.\r<BR>\n" );
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document.write( "this is the same as the answer that they said is the correct answer.\r<BR>\n" );
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document.write( "it is, however, a reflection about the y-axis, and not a reflection about the x-axis.\r<BR>\n" );
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document.write( "your answer, though not perfect if the order of the translations is to be taken into account, is a reflection about the x-axis, and not the y-axis.\r<BR>\n" );
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document.write( "here's 5 graphs for you to ponder.\r<BR>\n" );
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document.write( "the first is the original equation.\r<BR>\n" );
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document.write( "the second is the equations after the shift left 4 units and down 3 units.\r<BR>\n" );
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document.write( "the third is the second equation after reflection about the x-axis.\r<BR>\n" );
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document.write( "the fourth is the second equation after the reflection about the y-axis.\r<BR>\n" );
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document.write( "the fifth is what your equation would have given you.\r<BR>\n" );
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document.write( "your equation would have given you a reflection abut the line y = -3, not the x-axis, which is the line y = 0.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/121301.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/121302.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/121303.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/121304.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/121305.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the graphing calculator i used is at www.desmos.com/calculator.\r<BR>\n" );
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document.write( "it's a good calculator once you learn how to use it.\r<BR>\n" );
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document.write( "it also helps you to visualize what you are going and the impact it has on the graph.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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