Answer:
We are asked to find which graph represents the graph of the piecewise-defined function g(x) given as:
g(x)= x^2-4 ; if x < -1
1 ; if -1≤ x ≤ 1
and x^2+4 ; if x>1
i.e. in the region (-∞,-1) we will get a graph of a quadratic function x^2-4.
in the region [-1,1] we will get a straight line y=1.
and the region (1,∞) again we will get a graph of a quadratic function x^2+4.
Also the graph of the function is discontinuous at 1 and -1.
since the limit of the function at x=-1 and at x=1 does not exist.
As at x=-1.
Left hand limit= -3 (x^2-4; at x=-1 gives -3)
and right hand limit =1.
Whereas at x=1.
left hand limit=1
and right hand limit=5 ( x^2+4=1+4 )