Determine the horizontal asymptote (are my answers correct?)

Question

1. y = x³+2x²-6 / x²

2. y=x⁴ +3x³ + x²-7 / x⁵-3x³+8

3. f(x) = 2x² / x²+3x-4

my answers:

1. 2x²/x² = 2 is the horizontal asymptote

2. 3x³ / -3x³ = -1 is the h.a

3. 2x² / x² = 2 is the h.a

are my answers correct? if not, what should i do differently?

Answer 1

1. The degree of the numerator is greater than the degree of the denominator (3 > 2), so there is no horizontal asymptote.

2. The degree of the denominator is greater than the degree of the numerator (5 > 4)so the horizontal asymptote is at y = 0.

3. The degrees are equal, so you are correct.