Question

For the given function, find the vertical and horizontal asymptotes f(x)= x2+3/ x2-9

Answer 1

Set the denominatior equal to zero to find vertical asymptotes. Horizontal take the highest degree of the top and divide it by the highest degree of the bottom.
${x}^{2} - 9 = 0 \\ {x}^{2} = 9 \\ x = 3 \\ x = - 3 \\ \\ \frac{ {x}^{2} }{ {x}^{2} } = 1 \\ y = 1$
Vertical: x=3, x=-3
Horizontal : y=1