How do you find the asymptotes for #f(x)= (4x^2+5)/( x^2-1)#?
To find vertical asymptote, you must set the denominator to 0 and then solve.
This can be factored as a difference of squares
Now for horizontal asymptotes, which are a little trickier.
To find these, you must look for the highest power (exponent) in both the numerator and the denominator. The highest power in both is
So, the horizontal asymptote occurs at
Plugging in 4 for
This proves that there is a horizontal asymptote at y = 4, because an asymptote is essentially and undefined line on the graph of a function.
- Identify all the asymptotes in
#g(x) = (5x^2 + 10x)/(2x^2 + 7x + 3)#