(a)

Find .

Observe the graph.

As  tends to ,  approaches to .

Hence .

(b)

Find .

Observe the graph.

As  tends to ,  approaches to .

Hence .

(c)

Find .

Observe the graph.

Left hand limit  :

As  tends to  from left side,  approaches to .

Hence .

Right hand limit  :

As  tends to  from right side,  approaches to .

Hence .

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

Therefore .

(d)

Find .

Observe the graph.

As  tends to  from left side,  approaches to .

Hence .

(e)

Find .

Observe the graph.

As  tends to  from right side,  approaches to .

Hence .

(f)

Vertical asymptote :

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

Observe the graph.

The vertical asymptotes are  and .

Horizontal asymptote :

The horizontal asymptote is a line equation, as the value of  approaches to either positive or negative infinity.

Observe the graph.

The horizontal asymptotes are  and .

(a) .

(b) .

(c) .

(d) .

(e) .

(f) The asymptote are , ,  and .