so we has quadratic function that opens up, means that the lowest value is the vertex and the highest value is infinity vertex is on the x axis, that means the lowest y value is 0 highest is infinity
but, we do g(x)=2-f(x-5) so see the translation from f(x) to 2-f(x-5) so multiply whole function by -1 (reflects the function over the x axis, means new range is from 0 to negative inifnity) -f(x) minus 5 from every x (moved to the right 5 units, doesn't change the range) -f(x-5) add 2 to whole funciton (moved up 2 units) means new range is from 2 to negative infinity