Question

Find the horizontal or oblique asymptote of f(x) = negative 2 x squared plus 3 x plus 6, all over x plus 1.

Answer 1

-2x + 5

Explanation:

A horizontal asymptote of a rational function occurs when the degree of polynomials in both numerator and denominator are equal.

Also, a slant or oblique asymptote of a rational function occurs when the polynomial in the numerator is a higher degree than the polynomial in the denominator.

We are given the rational function,
`f(x)=(-2x^(2)+3x+6 )/(x+1)`

As, the degree of numerator > degree of denominator. There is no horizontal asymptote.

Now,the first two terms in the quotient ( forming a linear function ) after dividing the polynomial is the equation of the oblique asymptote.

After dividing we get that, the quotient is -2x+5

Hence, the equation of the oblique asymptote is -2x+5.

Answer 2

For the answer to the question above I' ll provide the solutions below.
2x + 3
-------------------
x+1 | 2x^2 + 5x + 6
2x^2 + 2x
-------------
3x + 6
3x + 3
--------
3
So the answer on the oblique asymptote is y = 2x + 3.
I hope my answer helped you. Have a nice day!