Question

Graph the piecewise-defined function.

Answer 1

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)