Answer:
A
Step-by-step explanation:
To reflect a function over the x-axis, we multiply the function by -1. So, if f(x) is the original function, then -f(x) is the function across the x-axis.
To reflect a function over the y-axis, we multiply the inside of the function by -1. So, if f(x) is the original function, then f(-x) is the function across the x-axis.
We have:
[tex]f(x)=(x-1)^2+1[/tex]
Then:
[tex]f(-x)=(-x-1)^2+1=f ^\prime(x)[/tex]
We can see that the choice that resembles this is A. If we let:
[tex]f(-4x)=(-4x-1)^2+1[/tex]
This is a reflection over the y-axis followed by a horizontal compression by a factor of 4.
Hence, our answer is A.
