Question

Given the functions a(x) = 4x2 − x + 2 and b(x) = x + 1, identify the oblique asymptote of the function a of x over the function b of x.

Answer 1

$a(x)=4x^2-x+2 \\ b(x)=x+1 \\ \\ f(x)=\frac{a(x)}{b(x)}=\frac{4x^2-x+2}{x+1}$

You can find the oblique asymptote by dividing the polynomial in the numerator by the polynomial in the denominator. The asymptote is the result of the division, without the remainder.
Look at the picture.

The oblique asymptote is $y=4x-5$.