Question

Given the functions a(x) = 4x2 + 2x - 3 and b(x) = x - 1, identify the oblique asymptote of the function a of x over the function b of x?

Answer 1

4x+6 is the oblique asymptote.

Explanation:

we have to find the oblique asymptote for the given function :

`(4x^2+2x-3)/(x-1)`

Oblique asymptote case arises when degree of numerator is greater than denominator

We divide the numerator by denominator to find the oblique asymptote.

You can see the long division in the attachement.

The quotient will give an equation which will be our required oblique asymptote.

4x+6 is the oblique asymptote.

Answer 2

The oblique asymptote of a function is the quotient of dividing a polynomial by another function. In this case, we divide 4x2 + 2x -3 to x-1. Hence,
4x + 6 x-1 | 4x2 + 2x -3 -(4x2 -4x) 6x - 3 -(6x - 6) 3

Hence the oblique asymptote is equal to 4x + 6