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

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!

Answer 2

Answer:

-2x + 5

Step-by-step 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, $f(x)=\frac{-2x^{2}+3x+6 }{x+1}$

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.