Question

The function g(x)=-(x)^2+5. The function f(x)=-g(x+2).

Answer 1

Short Answer f(x) down 5 units, left 2 units and right side up from g(x)
Step One
Find out what -g(x+2) is.
There are two steps to this. The first is to deal with the minus sign
(g(x)) = - x^2 + 5. Be very careful what you do next. 
Put brackets around both terms on the right.
g(x) = (-x^2 + 5) Now put the minus sign in front of g(x) and another one in front of the brackets.
-g(x) = - (-x^2 + 5) Remove the brackets.
-g(x) = x^2 - 5 

Result
So far g(x) moves down 5 units and opens upward. 

Step Two
The second step is to see what the x + 2 does.
-g(x + 2) = (x + 2)^2 - 5

The final result is that the graph opens upward, moves left 2 spaces and down 5.

There is a graph enclosed to show you the key steps.
The red graph is g(x) = x^2 - 5
The blue graph is g(x+2) = (x+2)^2 - 5