In what ways can vertical, horizontal, and oblique asymptotes be identified? Please use your own example to identify.

Lets take an examplef(x) = [tex] \frac{5x+6}{x+1} [/tex]In a rational function, the function has vertical asymptotes when denominator =0.To find out vertical asymptote we will make denominator =0 , to find out for what value of x the function becomes undefined.x+1=0 so x=-1Hence vertical asymptote at x=-1In a rational function, horizontal asymptote can be find using the degrees . We have 3 cases• If Degree of numerator is less than the denominator degree then horizontal asymptote is y = 0.• If Degree of numerator is greater than denominator degree then there is no horizontal asymptote . if degree of numerator is greater by a margin of one then there there will be oblique asymptote.• if Degree of numerator is equal to the denominator degree then the horizontal asymptote is equal to the leading coefficient of numerator to the leading coefficient of denominator.In our examplef(x) = [tex] \frac{5x+6}{x+1} [/tex]Degree of numerator is 1 and degree of denominator is 1Both are equal so we take ratio of leading coefficients.So horizontal asymptote y = [tex] \frac{5}{1} =5 [/tex]Lets take another example[tex] f(x)= \frac{x^3+7}{x^2+3} [/tex]degree of numerator is greater than the denominator degree by a margin of one . so we will have oblique asymptote.We find oblique asymptote by long divisionBy long division we will get xSo oblique asympotote is y=x