(a)

The function is .

If is even, is symmetric with respect to -axis.

If is odd, is symmetric with respect to to the origin.

(b)

Horizontal asymptote :

term of the numerarator of the function is  Where  is non negative value.

term of the denominator function is .

The horizontal asymptote exist when the degree of numerator is less than the degree of denominator.

Thus, the horizontal asymptote exist if and .

(c)

Horizontal asymptote will only appear when the greatest exponent of the numerator is either equal or less than the greatest exponent of the denominator.

So consider .

The function is .

The value of .

Thus, when the value of is .

(d)

Consider .

The function is .

Oblique asyptote or slant asymptote exists when the greatest exponent of the numerator is greater than the denominator.

When , the slant asymptote is .

(a)

If is even, is symmetric with respect to -axis.

If is odd, is symmetric with respect to to the origin.

(b)

The horizontal asymptote exist if and .

(c)

The horizontal asymptote exist if and .

(d)

When , the slant asymptote is .