Find the horizontal or oblique asymptote of f(x)= -2x^2+3x+6/x+2

There is no horizontal asymptote for this function but there is an oblique asymptote which is -2x + 7

Step-by-step explanation:

When given a function, it is very easy to check its horizontal asymptote,

When dealing with a function say;  

where a and b represents the leading coefficient, m and n represents the degrees, then to find the horizontal asymptote all we need to do is to compare the degree of the polynomials

If m < n then y= 0 That is, if the top degree is less than the bottom degree then the horizontal asymptote is zero(0)

If m = n then y =  

That is, if the top degree is equal to the bottom degree, then the horizontal asymptote  is equal to    where  a and b are coefficients of  

and

respectively.

If m > n then there is no horizontal asympto

te. That is, if the top degree is greater than the bottom degree, then there is no horizontal asymptote.

Which means there is only a slant asymptote or oblique asymptote

To find the slant asymptote, all we need to do is to use long division to divide our polynomials;

           -2x + 7______

x + 2    √-2x² + 3x + 6

    -___(-2x - 4x)_____

                   7x  + 6

                  - (7x +14)

___________________

                            -8

Therefore the oblique asymptote is -2x + 7

this shows a reflection over the x-axis and is translated one unit down and 6 units to the right (x + 6, y - 1)

hope this !

~just a girl in love with shawn mendes

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step-by-step explanation:

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