(a)

Find . 

Observe the graph.

Left hand limit : 

As  tends to  from left side,  approaches to negative large number.

So . 

Right hand limit : 

As tends to from right side, approaches to negative large number.

So . 

Left hand limit and right hand limit are equal, is exist.

. 

(b)

Find . 

Observe the graph.

Left hand limit : 

As  tends to  from left side,  approaches to positive large number.

So . 

Right hand limit : 

As tends to  from right side, approaches to positive large number.

So . 

Left hand limit and right hand limit are equal, is exist.

. 

(c)

Find . 

Observe the graph.

Left hand limit : 

As tends to from left side, approaches to positive large number.

So . 

Right hand limit : 

As tends to from right side, approaches to positive large number.

So . 

Left hand limit and right hand limit are equal, is exist.

. 

(d)

Find . 

Observe the graph.

As tends to from left side, approaches to negative large number.

So . 

(e)

Find . 

Observe the graph.

As tends to from right side, approaches to positive large number.

So . 

(f)

Find the vertical asymptote.

Vertical asymptote :

The vertical asymptote is a line equation, toward which a function approaches to either positive or negative infinity.

Observe the graph.

As tends to from left side, approaches to negative large number.

So . 

As tends to from left side, approaches to positive large number.

So . 

As tends to from right side, approaches to positive large number.

So . 

As tends to from left side, approaches to negative large number.

So . 

From the above statements, it satisfies the definition of vertical asymptotes.

The vertical asymptotes are , , , , and . 

(a) . 

(b) . 

(c) . 

(d) . 

(e) . 

(f) The vertical asymptotes are , , and .