Question

State the horizontal asymptote of the rational function. f(x) =(x+9)/(x^2+8x+5)

Answer 1

the degree of the numerator is 1, the degree of the denominator is 2
since the denominator has a larger degree, the horizontal asymptote is \(y=0\)

Answer 2

to find the vertical asymptotes, set \(x^2+8x+5=0\) and solve for \(x\)

Answer 3

this one doesn't factor, but you can complete the square easily
\[x^2+8x+5=0\]
\[x^2+8x=-5\]
\[(x+4)^2=-5+16=11\]
\[x+4=\pm\sqrt{11}\]
\[x=-4\pm\sqrt{11}\]

Answer 4

look at first post, answer is there