Question

How do you find vertical, horizontal and oblique asymptotes for `y =(3/x)+2`?

Answer 1

Vertical asymptote: `x = 0`
Horizontal asymptote: `y = 2`
Oblique asymptote: none

Explanation:

Find a common denominator for the function:
`y = 3/x +(2x)/x = (3+2x)/x = (2x+3)/x`

Rational Function: `(N(x))/(D(x))`, when `N(x) = 0` gives x-intercepts,
when `D(x) = 0` you find vertical asymptotes.

Vertical asymptote at `x = 0`

When `(N(x))/(D(x)) =( a_nx^n+....)/(b_mx^m+....)` where `n, m` are the degrees of the polynomials.

If `n=m` horizontal asymptote is at `y=a_n/b_m`

`n = m = 1`, so Horizontal asymptote: `y = 2/1; y = 2`

To have an oblique or slant asymptote, `m+1 = n` which is not the case, so there is no oblique asymptote.