Classifying Discontinuities

For each of the functions below, find all points of discontinuity, and classify them as removable discontinuities, jump discontinuities, vertical asymptotes, or other essential discontinuities.

1.

f(x) =

x3 - 2x2 - x + 2

3.

f(x) =

tan(2x)

x-2

4.

f(x) =

tan(1/x)

2.

f(x) =

{

x2 - 4 + 1/x

for x < 1

5.

f(x) =

{

2x + 4

for x < 2

-2

for x = 1

7

for x = 2

x - 3

for 1 < x 4

x3

for x > 2

3 - sqrt(x)

for x > 4

6.

7.

8. The table below gives values for a function. Where is this function discontinuous, and what kind of discontinuity is at each discontinuous point?