Answer:
We have to graph the piecewise-defined function:
f(x)= |x|-4 , if x < 0
-4 , if x ≥ 0
We know that if x <0 then |x| opens up as: -x.
Hence the function f(x) is defined as:
f(x)= -x-4 ; if x < 0
-4 ; if x ≥ 0.
Hence the graph of function f(x) is a linear graph of the type:
y= -x-4 in the interval (-∞,0)
and the graph of the function f(x) is a straight line passing through
y= -4 in the interval [0,∞).
Also the graph is continuous on whole of the real line as limit of the function exist at x=0 and is equal to the value of the function.
f(0)= -4
Hence, the graph is attached to the answer.
( The rest 3 graphs were given to be discontinuous)