For the function f(x) = –2(x + 3)2 − 1, identify the vertex, domain, and range.
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f(x) is a polynomial function (why? cuz it has whole number powers of x only, and no other complex terms), and a polynomial is always continuous on the interval (-∞,+∞).
that is for your domain.
the vertex of a parabola (your function is a parabola)
in a form of: f(x)=a(x-h)²+k
is the point: (h,k)
and the domain is all real numbers (as I have reviously explained)
Now, your leading coefficient is negative, that means your parabola opens down and goes into -∞.....
BUT, the range will be limited, and it is limited by the vertex because vertex is the maximum point (in any case when parabola opens down)
what is the y-value of your vertex?
that is where the range ends....
and it starts from negative infinity
Wouldn't the range be y is equal to or lesser than -3