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
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Answer and Explanation:
Given a function
f
(
x
)
which is a quadratic function whose graph is a parabola opening upwards and has a vertex on the x-axis. Hence the range of the function is
R
f
=
[
0
,
∞
)
Hence, function
y
(
x
)
=
−
f
(
x
)
is simply the parabola opening downwards, which is shifted 5 units. But still the range is not affected by the shift.
R
y
=
(
−
∞
,
0
]
Now, by adding 2 as a constant, we get the function g(x) and hence the range of g is,
R
g
=
(
−
∞
,
0
+
2
]
=
(
−
∞
,
2
]
Step-by-step explanation:
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