Final answer:
The function g(x) = - (x - 3)^2 + 5 represents a vertical reflection and translations both horizontally and vertically, without any vertical stretch or compression.
Step-by-step explanation:
The function g(x) = - (x - 3)^2 + 5 involves multiple transformations of the parent function f(x) = x^2. First, a vertical reflection is applied because of the negative sign in front of the quadratic term. This reflects the graph vertically downward in the coordinate system. Next, there is no vertical stretch or compression indicated because the coefficient of the quadratic term is 1 (after considering the negative sign for direction), implying the graph maintains its standard width. Lastly, the function is shifted horizontally to the right side of the coordinate system by 3 units due to the (x - 3) term, and translated vertically upward by 5 units because of the +5 at the end of the function.
In summary, this transformation does not involve a vertical stretch or compression (making the graph narrower or wider) but does involve reflection and translation.