Question

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

Answer 1

Answer: ( - infinity , 2]
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Answer 2

ragne is how far the y goes up and dlwon


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




range is (-∞,2]