SOLUTION: teacher wants 2 very different ways to transform/translate graph of log(8-x)? I found one way using two steps, but I need a second way using 1 step. log(-1)(x-8)= log(-1) + log(x

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: teacher wants 2 very different ways to transform/translate graph of log(8-x)? I found one way using two steps, but I need a second way using 1 step. log(-1)(x-8)= log(-1) + log(x      Log On


   

Question 239310: teacher wants 2 very different ways to transform/translate graph of
log(8-x)? I found one way using two steps, but I need a second way using 1 step.
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??
Answer by jsmallt9(3758) About Me  (Show Source):
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

Another way could be to factor out -1:
y+=+log%28%28%28-1%29%28x-+8%29%29%29
Factor the -1 into 10*(-1/10):
y+=+log%28%28%2810%29%28-1%2F10%29%28x-+8%29%29%29
Separate out the factor of 10:
y+=+log%28%2810%29%29+%2B+log%28%28%28-1%2F10%29%28x-+8%29%29%29
Since log%28%2810%29%29+=+1:
y+=+1+%2B+log%28%28%28-1%2F10%29%28x-+8%29%29%29
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)

I don't know if this second one is "very different" enough.