The function is , at and .

The function is , at .

Continuity Test condition 1:

Find if exists.

Substitute in .

The function is undefined at .

Continuity Test condition 2:

Find if exists.

Make a table that shows the values of for -values approaching from

the left and from the right.

Observe the table:

As tends to from the left approaches to .

As tends to from the right, approaches to .

and .

Since, limit exist.

.

Continuity Test condition 3: Check.

Observe above two conditions,

and is undefined.

Because , has an infinite discontinuity at .

has an infinite discontinuity at .

The function is , at .

Continuity Test condition 1:

Find if  exists.

Substitute in .

The function is defined for .

Continuity Test condition 2:

Find if exists.

Construct a table that shows the values of for -values approaching from

the left and from the right.

Observe the table:

As tends to from the left approaches to .

As tends to from the right, approaches to .

.

Continuity Test condition 3: Check.

Observe above two conditions,

Since , is continuous at .

has an infinite discontinuity at .

is continuous at .