
To sketch the graph of this function, we plot the points and lines as follows:

1.
: The limit as x approaches -4 from the left side. Since the function is continuous at -4, the limit exists and is equal to the value of the function at that point. So,
.
2.
: The limit as x approaches -4 from the right side. Again, since the function is continuous at -4 , the limit exists and is equal to the value of the function at that point. So,
.
3.
: The limit as x approaches -4. Since the left and right limits both exist and are equal, the overall limit exists and is equal to the common value. So,
.
4.
: The limit as x approaches 4. Since the function has a discontinuity at
(a jump from
to (-2), the limit does not exist. So,
is DNE.
5.
: The limit as x approaches 4 from the right side. Since the function is continuous at 4, the limit exists and is equal to the value of the function at that point. So,
.
6.
: The limit as x approaches 4 from the right side, multiplied by
. Since the function is continuous at 4, we can evaluate this limit by substituting
.
That's it!