Question

How do you identify the oblique asymptote of `f(x) = (x - 1)/(4x^2 + 2x - 3)`?

Answer 1

That function does not have an obliques asymptote. It does have horizontal asymptote `y=0`.

Explanation:

A rational function has an oblique asymptote if and only the quotient upon dividing is linear with slope `!= 0`.
The quotient is linear if and only if the degree of the numerator is one more than the degree of the denominator.

In the function for this question the degree of the numerator is less than that of the denominator, so, as `x` increases without bound, `f(x)` gets closer and closer to `0`.