document.write( "Question 1181202: The parent function f(x)=log10x is vertically stretched by a factor
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Algebra.Com's Answer #811075 by ikleyn(52810)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "The parent function f(x)=log10x is
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\n" ); document.write( "\n" ); document.write( "What is the equation of the vertical asymptote of the transformed function?
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\n" ); document.write( "\n" ); document.write( "            First,  look how I edited your post to make words/terms usage  CONSISTED  and mathematically correct.\r
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\n" ); document.write( "\n" ); document.write( "            Second,  when we solve such problem,  there is  NO  NEED  to trace the concrete \r
\n" ); document.write( "\n" ); document.write( "            function  f(x)=log10x  behavior/transformations/changes,\r
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\n" ); document.write( "\n" ); document.write( "            We should trace/analyse/follow the behavior of the vertical asymptote,  ONLY.\r
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document.write( "So, I look for changes of the vertical asymptote, ONLY, at each given step.\r\n" );
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document.write( "(a)  Vertical stretch by a factor of 3 DOES NOT CHANGE vertical asymptote x= 0.\r\n" );
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document.write( "     After this step, the asymptote REMAINS to be vertical x= 0.\r\n" );
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document.write( "(b)  Reflection in the y-axis DOES NOT CHANGE vertical asymptote x = 0.\r\n" );
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document.write( "     After this step, the asymptote REMAINS to be vertical x= 0.\r\n" );
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document.write( "(c)  Horizontal shift 4 units to the left  DOES CHANGE vertical asymptote x = 0.\r\n" );
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document.write( "     After this step, the asymptote BECOMES to be vertical x= -4.\r\n" );
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document.write( "(d)  Vertical shift 2.5 units up DOES NOT CHANGE vertical asymptote x= - 4.\r\n" );
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document.write( "     After this step, the asymptote REMAINS to be vertical x= -4.\r\n" );
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document.write( "ANSWER.  After all the listed transformations, the original vertical asymptote x= 0 becomes vertical asymptote x= -4, finally.\r\n" );
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document.write( "         It is true not only for the given parent function f(x).  \r\n" );
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document.write( "         With the given steps, it is true for ANY OTHER parent function with the vertical asymptote x= 0: \r\n" );
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document.write( "             for example, for the parent function y = f(x) = \"1%2Fx\".\r\n" );
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The post-solution note

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