help.

Question

Answer 1

(3_a)

Step 1:

The function is .

Find .

Take out as a common factor from the numerator and denominator.

As   then .

Solution :

Answer 2

(3_b)

Step 1:

The function is .

Find .

Take out as a common factor from the numerator and denominator.

As   then .

Solution :

Answer 3

(3_c)

Step 1:

The function is .

Find horizontal asymptotes of .

Definition of a Horizontal Asymptote :

The line is a horizontal asymptote of the graph of when or .

Take out as a common factor from the numerator and denominator.

As   then .

Therefore is a horizontal asymptotes of .

Solution :

Horizontal asymptote is .

 

Answer 4

(4_a)

Step 1:

The function is .

Find .

Take out  as a common factor from the numerator and denominator.

As   then .

Solution :

Answer 5

(4_b)

Step 1:

The function is .

Find .

Take out  as a common factor from the numerator and denominator.

As   then .

Solution :

Answer 6

(4_c)

Step 1:

The function is .

Find horizontal asymptotes of .

Definition of a Horizontal Asymptote :

The line is a horizontal asymptote of the graph of when or .

Take out  as a common factor from the numerator and denominator.

As   then .

Therefore is a horizontal asymptotes of .

Solution :

Horizontal asymptote is .

Answer 7

(5_a)

Step 1:

The function is .

Find .

Take out as a common factor from the numerator and denominator.

As   then .

Here as ,

Solution :

Answer 8

(5_b)

Step 1:

The function is .

Find .

Take out as a common factor from the numerator and denominator.

As  then .

Here as ,

Solution :

Answer 9

(5_c)

Step 1:

The function is .

Find horizontal asymptotes of .

Definition of a Horizontal Asymptote :

The line is a horizontal asymptote of the graph of when or .

Take out as a common factor from the numerator and denominator.

As  then .

Therefore is a horizontal asymptotes of .

Solution :

Horizontal asymptote is .