Answer:
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;
![f(x)=\frac{ax^{m} -------}{ax^{n} -------}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7Bax%5E%7Bm%7D%20-------%7D%7Bax%5E%7Bn%7D%20-------%7D)
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;
<u>-2x + 7______</u>
x + 2 √-2x² + 3x + 6
<u>-___(-2x - 4x)_____</u>
7x + 6
- (7x +14)
<u>___________________</u>
-8
Therefore the oblique asymptote is -2x + 7