Answer:
- Domain = [tex]R\ (\text{All real numbers})[/tex]
- Range = [tex]f\ \epsilon\ R\ :\ f\le -2}[/tex]
Step-by-step explanation:
The given function is,
[tex]f\left(x\right)=-\left(x+3\right)^2-2[/tex]
f(x) is a quadratic function. As this is a polynomial function, so its domain is the entire real number set.
As its leading coefficient will be negative, so it will open downward. Hence, its range will be all real numbers below its vertex.
The general vertex form of quadratic function or parabola is,
[tex]f(x)=a(x-h)^2+k[/tex]
where (h, k) is the vertex.
Comparing the given function with this we get the vertex at [tex](-3,-2)[/tex]
The y coordinate of the vertex is -2, so the range of the given quadratic function is,
[tex]f\ \epsilon\ R\ :\ f\le -2}[/tex]
