Find the oblique asymptote of the function.

Question

y = 2x^2 + 4x - 9/3 - x

Answer 1

y = (2x² + 4x - 9)/(3 - x) = - 2x -10 + 21/(3 - x). from here y = - 2x - 10 is oblique asymptote

Answer 2

Divide 2x² + 4x - 9 by -x + 3 to get a quotient of -2x - 10 with remainder 21.

So, the given function can be expressed as -2x - 10 + 21 / (-x+3).

As x goes to plus or minus infinity, 21 / (-x+3) goes to zero.

The oblique (or slant) asymptote is y = -2x - 10.