F is a quadratic function whose graph is a parabola opening upward and has a vertex on the x-axis. The graph of the new function g defined by g (x) = 2 - f (x - 5) has a range defined by the interval

A. [ - 5, + infinity)

B. [ 2, + infinity)

C. ( - infinity, 2]

D. ( - infinity, 0]

To move a function c units up, add c to the whole function

to reflect the function over the x axis, times the whole function by - 1

to move the graph c units to the right, minus c from every x

we got

from f (x)

we minused 5 from every x

to get f (x-5) moved graph 5 units to right

then we multiplied by - 1 to reflect across the x axis

to get - f (x-5)

then we added 2 to the whole thing to move it up 2 units to get

2-f (x-5)

so

range=lowest y value to highest y value

original paraobla opend up so original range is 0 to infinity

the original parabola was move 5 to the right, reflected across the x axis then moved up 2 units

originally, the vertex was on the x axis so range is not affected

then we reflected across x axis

so now range is negative infinity to 0

then we moved up 2 units

now range is negative infity to 2

so answer si C

with a movement 5 to the right, the vertex is still on the x axis