document.write( "Question 147685: If g(x) is a logarithmic function, then what effect does 'c' have on g(x) if f(x) = g(cx)?
\n" ); document.write( "a. g(x) shifts c units to the sign opposite of c
\n" ); document.write( "b. g(x) stretches or shrinks horizontally
\n" ); document.write( "c. g(x) stretches vertically
\n" ); document.write( "d. There is no effect on g(x)
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #108089 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
If g(x) is a logarithmic function, then what effect does 'c' have on g(x) if f(x) = g(cx)?
\n" ); document.write( "a. g(x) shifts c units to the sign opposite of c
\n" ); document.write( "b. g(x) stretches or shrinks horizontally
\n" ); document.write( "c. g(x) stretches vertically
\n" ); document.write( "d. There is no effect on g(x)
\n" ); document.write( "
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document.write( "This is a poorly written problem.  If 'c' were = 1 then there\r\n" );
document.write( "is no effect and the answer would be d.  If 'c' were negative \r\n" );
document.write( "there would also be a reflection across the y-axis.  But none\r\n" );
document.write( "of the answers allows for this. \r\n" );
document.write( "\r\n" );
document.write( "Here is the graph of  \r\n" );
document.write( "\r\n" );
document.write( "\"g%28x%29+=+log%283%2C%28x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%283%2Cx%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Here is the graph of  \r\n" );
document.write( "\r\n" );
document.write( "\"f%28x%29+=+g%282x%29=log%283%2C%282x%29%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%283%2C2x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "You can see that the the second graph has been shrunk horizontally.\r\n" );
document.write( "\r\n" );
document.write( "--------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Here is the graph of  \r\n" );
document.write( "\r\n" );
document.write( "\"g%28x%29+=+log%282%2C%28x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%283%2Cx%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Here is the graph of  \r\n" );
document.write( "\r\n" );
document.write( "\"f%28x%29+=+g%280.5x%29=log%282%2C%280.5x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%283%2C0.5x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "You can see that the the second graph has been stretched horizontally.\r\n" );
document.write( "\r\n" );
document.write( "-------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Here is the graph of  \r\n" );
document.write( "\r\n" );
document.write( "\"g%28x%29+=+log%284%2C%28x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%284%2Cx%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Here is the graph of  \r\n" );
document.write( "\r\n" );
document.write( "\"f%28x%29+=+g%28-2x%29=log%284%2C%28-2x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%284%2C-2x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "You can see that the the second graph has been shrunk horizontally\r\n" );
document.write( "and reflected across the y-axis.\r\n" );
document.write( "\r\n" );
document.write( "----------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Here is the graph of  \r\n" );
document.write( "\r\n" );
document.write( "\"g%28x%29+=+log%285%2C%28x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%285%2Cx%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Here is the graph of  \r\n" );
document.write( "\r\n" );
document.write( "\"f%28x%29+=+g%280.5x%29=log%285%2C%28-0.5x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Clog%285%2C-0.5x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "You can see that the the second graph has been stretched horizontally\r\n" );
document.write( "and reflected across the y-axis.\r\n" );
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document.write( "Therefore, the correct choice is probably (b), but that does not tell \r\n" );
document.write( "about the fact that if c is negative there is also a refection across the\r\n" );
document.write( "y-axis\r\n" );
document.write( "\r\n" );
document.write( "There is no effect when \"c=1\"\r\n" );
document.write( "There is a horizontal shrink when \"c%3E1\"\r\n" );
document.write( "There is a horizontal stretch when \"0%3Cc%3C1\"\r\n" );
document.write( "There is both a horizontal shrink and a refection across the y-axis when \r\n" );
document.write( "\"c%3C-1\"\r\n" );
document.write( "There is a horizontal stretch and a reflection across the y-axis when \"-1%3Cc%3C0\"\r\n" );
document.write( "There is only a reflection across the y-axis when \"c=-1\"\r\n" );
document.write( "\r\n" );
document.write( "More of these possibilities involve horizontal shrinks and stretches, so \r\n" );
document.write( "your teacher probably intended for the correct choice to be b.\r\n" );
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document.write( "Edwin
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