Answer:
A) [tex]y=-5x-4[/tex]
B) [tex]y=-5x+4[/tex]
C) [tex]y=\frac{x-4}{5}[/tex]
Step-by-step explanation:
So we have the equation:
[tex]y=5x+4[/tex]
Let's write this in function notation. Thus:
[tex]y=f(x)=5x+4[/tex]
A)
To flip a function over the x-axis, multiply the function by -1. Thus:
[tex]f(x)=5x+4\\-(f(x))=-(5x+4)[/tex]
Simplify:
[tex]-f(x)=-5x-4[/tex]
B) To flip a function over the y-axis, change the variable x to -x. Thus:
[tex]f(x)=5x+4\\f(-x)=5(-x)+4[/tex]
Simplify:
[tex]f(-x)=-5x+4[/tex]
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):
[tex]f(x)=5x+4[/tex]
Switch:
[tex]x=5f^{-1}(x)+4[/tex]
Subtract 4 from both sides:
[tex]x-4=5f^{-1}(x)[/tex]
Divide both sides by 5:
[tex]f^{-1}(x)=\frac{x-4}{5}[/tex]
And we're done :)
