How do you find the asymptotes for #(2x^6 + 6x^3 )/( 4x^6 + 3x^3)#?
When we want to find the horizontal asymptotes, we want to analyze the highest degrees on the top and bottom.
Since we have the same degree on the top and bottom, the horizontal asymptote just simplifies to the coefficients. We're left with
For our vertical asymptote, we want to think about what value(s) make our function defined.
We can set the denominator equal to zero. We get
We can factor our an
Setting both factors equal to zero, we get
These are our vertical asymptotes.
Hope this helps!