Answer:
A) ![y=-5x-4](https://tex.z-dn.net/?f=y%3D-5x-4)
B) ![y=-5x+4](https://tex.z-dn.net/?f=y%3D-5x%2B4)
C) ![y=\frac{x-4}{5}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bx-4%7D%7B5%7D)
Step-by-step explanation:
So we have the equation:
![y=5x+4](https://tex.z-dn.net/?f=y%3D5x%2B4)
Let's write this in function notation. Thus:
![y=f(x)=5x+4](https://tex.z-dn.net/?f=y%3Df%28x%29%3D5x%2B4)
A)
To flip a function over the x-axis, multiply the function by -1. Thus:
![f(x)=5x+4\\-(f(x))=-(5x+4)](https://tex.z-dn.net/?f=f%28x%29%3D5x%2B4%5C%5C-%28f%28x%29%29%3D-%285x%2B4%29)
Simplify:
![-f(x)=-5x-4](https://tex.z-dn.net/?f=-f%28x%29%3D-5x-4)
B) To flip a function over the y-axis, change the variable x to -x. Thus:
![f(x)=5x+4\\f(-x)=5(-x)+4](https://tex.z-dn.net/?f=f%28x%29%3D5x%2B4%5C%5Cf%28-x%29%3D5%28-x%29%2B4)
Simplify:
![f(-x)=-5x+4](https://tex.z-dn.net/?f=f%28-x%29%3D-5x%2B4)
C) A reflection over the line y=x is synonymous with finding the inverse of the function.
To find the inverse, switch x and f(x) and solve for f(x):
![f(x)=5x+4](https://tex.z-dn.net/?f=f%28x%29%3D5x%2B4)
Switch:
![x=5f^{-1}(x)+4](https://tex.z-dn.net/?f=x%3D5f%5E%7B-1%7D%28x%29%2B4)
Subtract 4 from both sides:
![x-4=5f^{-1}(x)](https://tex.z-dn.net/?f=x-4%3D5f%5E%7B-1%7D%28x%29)
Divide both sides by 5:
![f^{-1}(x)=\frac{x-4}{5}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Cfrac%7Bx-4%7D%7B5%7D)
And we're done :)
Answer:
The answer is
.
Step-by-step explanation:
☆Remember:
![slope = \frac{rise}{run}](https://tex.z-dn.net/?f=slope%20%3D%20%20%5Cfrac%7Brise%7D%7Brun%7D%20)
▪Happy To Help <3