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---> 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]
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graph of f(X) looks like this.
-f(X) will be inverted.
by adding 2 to -f(X), graph shifts up by two units
if we replace X by x-5 the graphs shifts along X axis.
so the range remains same as that of 2-f(X).
so the range of g(X) is (-infinity,2]
option C
-f(X) will be inverted.
by adding 2 to -f(X), graph shifts up by two units
if we replace X by x-5 the graphs shifts along X axis.
so the range remains same as that of 2-f(X).
so the range of g(X) is (-infinity,2]
option C
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f (x) = x^2 (given function)
which has range =[0, ∞)
new f (g) = 2-(x-5)^2
which has range =(-∞,2]
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