​ algebra 2 help

By the way, f(x)= |x-2|-5

(1/2) f (x - 2)  =  (1/2)  ( l  (x - 2) - 2 l - 5 )   =  (1/2) l x - 4 l   - 5/2   =  g(x)

To find the y intercept, let x  = 0  and we have

y  = (1/2)  l 0 - 4 l - 5/2  = (1/2) (4) - 5/2  =  2 - 5/2  =  -1/2

To find the x intercepts, let y  =  0

0  = (1/2) l x - 4 l  - 5/2   multiply through by 2

0  = l x  - 4  l - 5    add 5 to both sides

5  =  l x - 4  l

So either   

x  - 4  = 5    or             x  - 4   =  -5

x  = 9          or             x  = -1