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.

Construct a table that shows the values of for -values approaching from the left and from the right. 

Observe the table values, as tends to from the left and from the right, approaches to .

.

Continuity Test condition 3: Check.

Observe above two conditions,

exist and is undefined.

Because , is discontinuous at .

has a removable 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 end from the right. 

Observe the table values, as tends to from the left and from the right, approaches to .

.

Continuity Test condition 3: Check.

Observe above two conditions,

Because , is continuous at .

has a removable discontinuity at .

is continuous at .