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

1 Answer
Mar 31, 2017

Answer:

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]