document.write( "Question 239310: teacher wants 2 very different ways to transform/translate graph of
\n" ); document.write( "log(8-x)? I found one way using two steps, but I need a second way using 1 step.
\n" ); document.write( "log(-1)(x-8)= log(-1) + log(x-8)....log(x-8) is a horizontal shift to right, but log(-1) is not defined, so is this OK?? \n" ); document.write( "
Algebra.Com's Answer #175732 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
Factoring out the minus -1 was a good idea. But, as you found, separating log(-1) was not. With \"y+=+log%28%28%28-1%29%28x-8%29%29%29\", the transformation from \"y+=+log%28%28x%29%29\" is:
  • A translation to the right of 8
  • A reflection in the y-axis

\n" ); document.write( "Another way could be to factor out -1:
\n" ); document.write( "\"y+=+log%28%28%28-1%29%28x-+8%29%29%29\"
\n" ); document.write( "Factor the -1 into 10*(-1/10):
\n" ); document.write( "\"y+=+log%28%28%2810%29%28-1%2F10%29%28x-+8%29%29%29\"
\n" ); document.write( "Separate out the factor of 10:
\n" ); document.write( "\"y+=+log%28%2810%29%29+%2B+log%28%28%28-1%2F10%29%28x-+8%29%29%29\"
\n" ); document.write( "Since \"log%28%2810%29%29+=+1\":
\n" ); document.write( "\"y+=+1+%2B+log%28%28%28-1%2F10%29%28x-+8%29%29%29\"
\n" ); document.write( "The transformations from \"y+=+log%28%28x%29%29\" would be:
  • A translation to the right of 8
  • A translation up of 1
  • A reflection in the y-axis (because of the \"-\")
  • A horizontal spreading or stretching by a factor of 10 (Stretching, not compression, because of the fraction)

\n" ); document.write( "I don't know if this second one is \"very different\" enough.\r
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