Asymptotes are lines that come close but never touch a function.

There are horizontal, vertical, and slanted asymptotes.

HA- y=k

VA- x=k

slanted(oblique asymptote)-y=mx+b

Horizontal asymptote of rational functions:

If both polynomials have the same degree: Divide the coefficients of the leading terms, this is your asymptote. (y)

If the degree of the numerator is less than the denominator, the asymptote is located at y=0.

If the degree of the denominator is less than the numerator, there is no asymptote.

Vertical asymptote of rational functions:

It cancels because (x+3) is above it, therefore, it cancels out. Use equation solving or quadratic formula to find out.

Oblique asymptotes:

Divide the numerator by the denominator long division to get your y=mx+b form. What's on top is your asymptote.