Observe the graph of the function.

(a) 

We can observe from the graph that  undefined.

The Vertical asymptote at  indicates that function is undefined.

 is undefined.

(b) 

We can observe from the graph that  does not exists.

The function has a vertical asymptote at .

Vertical Asymptote means the zeroes of the denominator.

As  tends to  from the left hand side,  tends to .

As  tends to  from the right hand side,  tends to .

Since the left hand limit and right hand limit are not equal, limit does not exist

at .

 does not exist.

(c) 

We can observe from the graph that  exists.

The solid dot indicates that value of the function exist at .

.

(d) 

We can observe from the graph that  does not exists.

As  tends to  from the left hand side,  tends to .

As  tends to  from the right hand side,  tends to .

Since the left hand limit and right hand limit are not equal, limit does not exist

at .

 does not exist.

(e) 

We can observe from the graph that  does not exists.

The hollow dot indicates that value of the function does not exist at .

 is undefined.

(f) 

We can observe from the graph that  exists.

As  tends to  from the left hand side,  tends to .

As  tends to  from the right hand side,  tends to .

Since the left hand limit and right hand limit are equal, limit exist at .

.

(g) 

We can observe from the graph that  exists.

The solid dot indicates that value of the function exist at .

.

(h) 

As  tends to 4 from the left hand side,  tends to .

As  tends to 4 from the right hand side,  tends to .

Since the left hand limit and right hand limit are undefined, limit does not exist

at .

 does not exist.

(a)  is undefined.

(b) does not exist.

(c) .

(d)  does not exist.

(e)  is undefined.

(f) .

(g) .

(h)  does not exist.