Question

Graph the piecewise-defined function.

Answer 1

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 )