Answer:
The answer is. C. [tex]f(x)=(x+8)^2-1[/tex]
Step-by-step explanation:
If we have a function f(x) then we can move its graph horizontally making the transformation [tex]y = f(x + c)[/tex]
Then if [tex]c> 0[/tex] the graph will move c units to the left.
If [tex]c <0[/tex] the graph will move c units to the right.
If we apply the transformation [tex]y = f(x) + h[/tex] then the graph of f(x) will move vertically h units.
If [tex]h> 0[/tex] the displacement will be h units up
If [tex]h <0[/tex] the displacement will be h units down.
In this problem we have the parent function [tex]y = x ^ 2[/tex] and we want to move 8 units to the left and 1 unit to the bottom.
Then we apply the transformations described above with [tex]c = 8[/tex].
[tex]y = f(x + 8) = (x + 8) ^ 2[/tex]
Now we must move the function 1 unit down, with [tex]h = -1[/tex].
[tex]y = f(x + 8) -1 = (x + 8) ^ 2 -1[/tex]
[tex]f(x)= (x + 8) ^ 2 -1[/tex]
The correct answer is option C
