Question

What is a vertical and horizontal asymptote?

Answer 1

Horizontal Asymptotes (y = #)

*Use degree of polynomials

P = Q y = a/b P & Q are polynomials
P < Q y = 0
P > Q None P(x)/Q(x)

ex. \[\frac{ 2x ^{2}-4x+8\ }{ 3x ^{2} - 1}\] P = Q because the exponents are the same. So, y = 2/3 because a is the numerator part and b is the denominator part.

ex. \[\frac{ 3x ^{4}-6x ^{2} +11}{ 5x ^{5} -1 }\] P < Q because 4 is less than 5. So it would be y = 0. Does this make sense to you?

Answer 2

Vertical Asymptotes:

ex. \[\frac{ x+1 }{ (x+2)(x-3)}\] \[x \neq -2, 3\] So the vertical asymptotes would be x = -2 and x = 3

ex. \[\frac{ (x-4)(x+1) }{ (x+1)(x-2) }\] Since there's (x+1) on the numerator and denominator, they are called holes. It's the "gap" in the graph. Your vertical asymptote would be x = 2