What is the domain and range of F(x) = -2(x + 3)² - 5?

1 Answer
Alan P. · George C.
Nov 22, 2015

Domain: (-oo,+oo) in RR
Range: (-oo,-5] in RR

Explanation:

F(x) = -2(x+3)^2-5 can be evaluated for all values of x in RR
so the Domain of F(x) is all RR

-2(x+3)^2-5
is a quadratic in vertex form with vertex at (-3,-5)
and the negative coefficient of (x+3)^2 tells us that the quadratic opens downward;
therefore (-5) is a maximum value for F(x)

Alternative way of seeing this:
(x+3)^2 has a minimum value of 0 (this is true for any squared Real value)
therefore
-2(x+3)^2 has a maximum value of 0
and
-2(x+3)^2-5 has a maximum value of (-5)

Second alternative
consider the graph of this function:
graph{-2*(x+3)^2-5 [-17.42, 5.08, -9.78, 1.47]}

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