anonymous
  • anonymous
Logistic parent function: 1/1+e^-x. What is the graph and function if 1/+e^-x is shifted left 1 unit? What is the graph and function if flipped over the x-axis?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[f(x) = \frac{ 1 }{ 1+e^{-x} }\]
SolomonZelman
  • SolomonZelman
when you shift a function C units right, you subtract C from every x. when you shift C units left, you add C to every x. --------------------------------------------- To reflect the function across the x-axis, mutliply the [entire] function times 1.
anonymous
  • anonymous
So would the function for shifting left one unit horizontally be: \[f(x) = 1/(1+e^x) + 1\]

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SolomonZelman
  • SolomonZelman
that would be shifted 1 unit up.
anonymous
  • anonymous
The one being under the fraction as well.
anonymous
  • anonymous
Sorry!
SolomonZelman
  • SolomonZelman
you add/subtract the C not from/to the function. you are subtracting/adding to/from the x.
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle f(x)=\frac{1 }{1+e^{-x}} }\) to shift to the left by 1 unit: \(\large\color{black}{ \displaystyle f(x)=\frac{1 }{1+e^{-(x+1)}} }\)
SolomonZelman
  • SolomonZelman
you are adding C to the x (jut as I did). And in this case, the "C" is 1.
anonymous
  • anonymous
I see! How would the over x axis function look?
SolomonZelman
  • SolomonZelman
you just multiply the entire function times -1, to reflcet over the x-axis.
SolomonZelman
  • SolomonZelman
to reflect*
anonymous
  • anonymous
So: \[f(x) = -1(\frac{ 1 }{ 1+e^-x }\]
anonymous
  • anonymous
Forgot the end parenthesis.
SolomonZelman
  • SolomonZelman
Yes, and that would be just same as \(\displaystyle \large \frac{-1}{1+e^{-\left(x+1\right)}}\)
anonymous
  • anonymous
Wow! Thank you, I understand now.
SolomonZelman
  • SolomonZelman
Anytime!

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