Help with vertical and horizontal asymptotes!!?

Question

1. y=x/x-3

2.y=x^2-9/x^3+3x^2-18x

3.y=x^2-2x+1/x^2-3x-4

how do i solve these showing each step please...thank you!!!

Answer 1

What is the question to "solve"?

Do you mean find the vertical/horizontal asymptotes? If so,

then

V.A. is when the denominator equals zero. We cannot use that value. H.A. is what happens to the value of the function as x approaches +/- infinity. **special case if both denominator and numerator equal zero, then it is not a VA but a "hole" in the graph**

1. VA x=3 and HA y=1

2.x^2 - 9 factors to (x-3)(x+3) and denom factors to x(x+6)(x-3), so the HA would be zero y=0 ; but since (x-3) will 'cancel' then it is simply a hole in the graph -- not in domain, but NOT a vertical asymptote. The only VA are x=0 and x = - 6

3.numerator is (x-1)(x+1) and denominator is (x-4)(x+1)

HA is y=1 and VA is ONLY x = 4 (since the other factor cancels)