Hi BeSweeet,

Speaking of PowerPoint, let me suggest that you check this out: Asymptote Tutorial

[1]

(a) No vertical asymptote because any real number is valid for x in the denominator.

(b) No horizontal asymptote because the degree of the numerator is not less than or equal to the degree of the denominator.

(c) Has a slant asymptote since the degree of the numerator is exactly one degree bigger than the denominator. Use long division to divide the denominator into the numerator and discard the remainder. The slant asymptote is at y=x-1

[2] Try to follow [1] to answer this one

[3]

(a) No vertical asymptote (see reason for [1] above)

(b) Has a horizontal asymptote since the degree of the numerator is equal to the degree of the denominator. The horizontal asymptote is y = a/b where a is the leading coefficient of the numerator and b is the leading coefficient of the denominator. Horizontal asymptote is y = 3

(c) No slant asymptote (see reason for [1] above)

[4]

(a) No vertical asymptote

(b) Has horizontal asymptote since degree of numerator is less than the degree of the denominator. Horizontal asymptote in this case is y = 0

(c) No slant asymptote.