document.write( "Question 152622: I have to describe the transformation on the following graph of f(x)=e^x. I also have to state the placement of the horizontal asymptote and y-intercept after the transformation. I'm lost and do not understand. The first transformation is g(x)=e^x-5 and
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Algebra.Com's Answer #112196 by Edwin McCravy(20062) $\"\"$ $\"About$

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have to describe the transformation on the following graph of f(x)=e^x. I also have to state the placement of the horizontal asymptote and y-intercept after the transformation. I'm lost and do not understand. The first transformation is g(x)=e^x-5 and the second is h(x)= -e^x
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document.write( "I cannot tell whether that first one is \r\n" );
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document.write( " or \r\n" );
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document.write( "So I'll do it both ways.\r\n" );
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document.write( "Here are the transformation rules:\r\n" );
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document.write( "Assume +k is a positive number and -k is a \r\n" );
document.write( "negative number.\r\n" );
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document.write( "1. Vertical shifts: \r\n" );
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document.write( "A. Adding +k to the right side of the equation of\r\n" );
document.write( "   a function shifts its graph UPWARD by k units.\r\n" );
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document.write( "B. Adding -k to the right side of the equation of\r\n" );
document.write( "   a function shifts its graph DOWNWARD by k units.\r\n" );
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document.write( "2. Horizontal shifts:\r\n" );
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document.write( "A. Replacing x in the right side of the equation of\r\n" );
document.write( "   a function by x+k shifts its graph to the LEFT by\r\n" );
document.write( "   k units.\r\n" );
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document.write( "B. Replacing x in the right side of the equation of\r\n" );
document.write( "   a function by x-k shifts its graph to the RIGHT by\r\n" );
document.write( "   k units.\r\n" );
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document.write( "3. Reflecting across axes:\r\n" );
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document.write( "A. Multiplying the right side of the equation of a\r\n" );
document.write( "function through by -1 reflects its graph in (or\r\n" );
document.write( "across) the x-axis  \r\n" );
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document.write( "B. Replacing x in the right side of the equation of\r\n" );
document.write( "a function by -x reflects its graph in (or across) \r\n" );
document.write( "the y-axis  \r\n" );
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document.write( " has y-intercept (0,1) and asymptote the\r\n" );
document.write( "vertical line  which is the x-axis.\r\n" );
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document.write( " to\r\n" );
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document.write( "Here g(x) is formed by replacing x in the right side of f(x)\r\n" );
document.write( "by x-5, so this is case 2B above, and thus the graph of g(x)\r\n" );
document.write( "is the graph of f(x) shifted to the RIGHT by 5 units.  \r\n" );
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document.write( "The y-intercept is shifted from (0,1) 5 units RIGHT to the\r\n" );
document.write( "point (5,1).  The horizontal asymptote is not affected when \r\n" );
document.write( "shifting right, so it is still y=0\r\n" );
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document.write( "--------------------\r\n" );
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document.write( "Here g(x) is formed by adding -5 to the right side of f(x),\r\n" );
document.write( "so this is case 1B above, and thus the graph of g(x)\r\n" );
document.write( "is the graph of f(x) shifted DOWNWARD by 5 units.\r\n" );
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document.write( "The y-intercept is shifted from (0,1) 5 units DOWNWARD to the\r\n" );
document.write( "point (0,-4).  The horizontal asymptote is shifted DOWNWARD\r\n" );
document.write( "from  (the x-axis) to the horizontal line .\r\n" );
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document.write( "--------------------\r\n" );
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document.write( "Here h(x) is formed by multiplying the right side of f(x)\r\n" );
document.write( "through by -1, a case of 3A. This reflects its graph in \r\n" );
document.write( "(or across) the x-axis.  The y-intercept (0,1) is reflected \r\n" );
document.write( "to its \"image point\" (0,-1) [thinking of the x-axis as a \r\n" );
document.write( "mirror].  The asymptote y=0 (the x-axis) is not affected by\r\n" );
document.write( "a reflection in the x-axis.\r\n" );
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document.write( "Edwin

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