Which graph represents the function? g(x)={x      if  x< 2−3   if  x≥2

We have to graph the function g(x) which is given as:

g(x)=  x when x<2

 and -3 when x ≥2.

Clearly after looking at the function we see that the function is not continuous since we find the continuity at x=2 as follows.

Left hand limitat 2:

g(2-h)=lim h→0 2-h

        =2-0=2

Also right hand limit at x=2 is:

g(2+h)=lim h→0 (2+h)

          = 2+0=2

Also g(2)= -3.

As:

Left hand limit= Right hand limit but is not equal to function's value at that point.

Hence, the function is discontinuous at x=2.

so for x<2 we will get a graph of a line y=x.

and for x≥2 we will get a straight line y=-3 parallel to the domain.