SOLUTION: Given the function y = f(x) = -x^2 + 8x -12. Suppose the domain of the function is restricted to the semi-open interval (3,7]. What is the corresponding range of the function in in

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Question 1096363: Given the function y = f(x) = -x^2 + 8x -12. Suppose the domain of the function is restricted to the semi-open interval (3,7]. What is the corresponding range of the function in interval notion?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Graph can make the range and domain a little easier to recognize.

graph%28300%2C300%2C-5%2C15%2C-15%2C5%2C-x%5E2%2B8x-12%29

Lowest point in range is at x=7.
-%287%29%5E2%2B8%2A7-12
-49%2B56-12
-5
Minimum of the range is AT f=-5


-1%28x%5E2-8x%2B12%29
-1%28x-6%29%28x-2%29
Roots at x=2 and x=6, so maximum f is at x=4.
-%284%29%5E2%2B8%284%29-12
-16%2B32-12
16-12
4--------maximum f.


RANGE of f:
-5 to +4.