How do you find vertical, horizontal and oblique asymptotes for #f(x)= (5x^2-17x-12)/(2x^2-7x-4)#?
The horizontal asymptote is
This problem is a bit tricky because there is a "hole" at
Start by factoring both numerator and denominator.
Note that factor
To find the asymptotes, use the function that results after the factor cancels.
To find the horizontal asymptote (HA), compare the degree of the numerator to the degree of the denominator.
If the degrees are the same, the HA is
If the degree of the denominator is greater, the HA is
If the degree of the numerator is greater, there is an oblique asymptote.
In this example, both the numerator and denominator have a degree of
The HA is then
There is no oblique asymptote, because the degree of the numerator is not greater than the degree of the denominator.
To find the vertical asymptote (VA), find the value of