Answer:
d). [tex]g(x)= (x -3)^{2} -1[/tex]
Step-by-step explanation:
The original function [tex]f(x) = x^{2}[/tex] began from the origin mean that when x=0 the is going to be y=0
Using the standard equation quadratic function:
[tex]y= a*(x-h)^{2} +k\\h= 3[/tex] , [tex]k=-1[/tex], [tex]a=1[/tex]
Solving:
[tex]y=1*(x-3)^{2} + (-1)\\y=(x-3)^{2} -1[/tex]
The second function have origin in the point (3,1) so making the function x=3
[tex]g(x)= (x -3)^{2}-1\\g(3)= (3 -3)^{2}-1\\ g(3)=-1[/tex]
