Question

HALP PLEASEEE

Find the horizontal or oblique asymptote of f(x) = 2 x squared plus 5 x plus 6, all over x plus 1

A) y = −1
B) y = −2
C) y = 2x + 3
D) y = −2x + 5

Answer 1

Remember that a rational function will have an oblique asymptote if the degree of the polynomial in the numerator is higher than the degree of the polynomial in the denominator. Since the degree of the numerator of our rational function is 2, and the degree of its numerator is 1, our function will have an oblique asymptote. To find it, we are going to use long division:

`(2x^(2) +5x+6)/(x-1) = 2x+3` with a remainder of 3.
The quotient of the division will be the terms of the linear equation that represents the oblique asympote of our function; notice that you don't need to use the remainder at all:

Equation of the oblique asymptote:

`y=2x+3`

We can conclude that the correct answer is C) y = 2x + 3.