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?

Question

anonymous · Answer

$$f(x) = \frac{ 1 }{ 1+e^{-x} }$$

solomonzelman · Answer

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 · Answer

So would the function for shifting left one unit horizontally be: $$f(x) = 1/(1+e^x) + 1$$

solomonzelman · Answer

that would be shifted 1 unit up.

anonymous · Answer

The one being under the fraction as well.

anonymous · Answer

Sorry!

solomonzelman · Answer

you add/subtract the C not from/to the function.

you are subtracting/adding to/from the x.

solomonzelman · Answer

$\large\color{black}{ \displaystyle f(x)=\frac{1 }{1+e^{-x}}  }$

to shift to the left by 1 unit:

$\large\color{black}{ \displaystyle f(x)=\frac{1 }{1+e^{-(x+1)}}  }$

solomonzelman · Answer

you are adding C to the x (jut as I did). And in this case, the "C" is 1.

anonymous · Answer

I see! How would the over x axis function look?

solomonzelman · Answer

you just multiply the entire function times -1, to reflcet over the x-axis.

solomonzelman · Answer

to reflect*

anonymous · Answer

So: $$f(x) = -1(\frac{ 1 }{ 1+e^-x }$$

anonymous · Answer

Forgot the end parenthesis.

solomonzelman · Answer

Yes, and that would be just same as

$\displaystyle \large \frac{-1}{1+e^{-\left(x+1\right)}}$

anonymous · Answer

Wow! Thank you, I understand now.

solomonzelman · Answer

Anytime!