Question

How do you find all the asymptotes for `f(x) = (3x^2 + 2x - 5)/(x - 4)`?

Answer 1

V.A. `x=4`
H.A. non
S.A. `3x+14`

Explanation:

. For a function to have vertical asymptote, the function needs to have undefined points also known as zeros of denominator.
`x-4`
`x=4` `<-` vertical asymptote

. When the degree of denominator is greater than the degree of the numerator the function will have a horizontal asymptote.
in this function degree of numerator is 2 and the degree of denominator is 1
`2>1` there fore this function does not have a horizontal asymptote

. to find slant asymptote, use polynomial long division

Slant Asymptote is `3x+14`