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Question

What is the range of f(x)=1x2+6x+6

A
(0,)
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B
(,13][0,)
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C
(13](0,)
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D
(,13](0,13]
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Solution

The correct option is C (13](0,)
x2 + 6x + 6 = x2 + 6x + 9 - 3 = (x+3)2 - 3
(x+3)23 has a range [3,)
We need to find the range of 1(x+3)23
Let us break the range of (x+3)23 into two ranges [-3, 0) and (0, ).
When (x+3)23 ranges from (0,), 1(x+3)23 ranges
from (0, )
When (x+3)23 ranges from [-3, 0), 1(x+3)23 ranges
from (,13]
Overall range = (,13](0,)

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