Question

How do you find the domain and range of `g(x)=-x^2-3x-1`?

Answer 1

Domain: `x in RR` . Range: `g(x)<=1.25`

Explanation:

`g(x)= -x^2-3x-1 , a= -1, b= -3 , c= -1`
Domain (possible value of x): Any real value i.e `x in RR`

Range: This is an equation of parabola , opening downwards, since `a` is negative.
Vertex(x) `= -b/(2a)= 3/ -2=-1.5`
Vertex(y) `g(x)= -(-1.5)^2 -3*(-1.5) -1 = 1.25`

Vertex is at `( -1.5 , 1.25) :. 1.25` is the maximum point.
Therefore Range, `g(x)<=1.25` graph{-x^2-3x-1 [-10, 10, -5, 5]} [Ans]