## anonymous one year ago 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?

1. anonymous

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

2. 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.

3. anonymous

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

4. SolomonZelman

that would be shifted 1 unit up.

5. anonymous

The one being under the fraction as well.

6. anonymous

Sorry!

7. SolomonZelman

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

8. SolomonZelman

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

9. SolomonZelman

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

10. anonymous

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

11. SolomonZelman

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

12. SolomonZelman

to reflect*

13. anonymous

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

14. anonymous

Forgot the end parenthesis.

15. SolomonZelman

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

16. anonymous

Wow! Thank you, I understand now.

17. SolomonZelman

Anytime!