Question

State the horizontal asymptote of the rational function.

f(x) = quantity nine x squared minus three x minus eight divided by quantity four x squared minus five x plus three.

y = 3/5

y = 9/4

y = 0

None

Answer 1

y=9/4

Explanation:

Answer 2

`f(x)= (9x^2-3x-8)/(4x^2-5x+3)`

Horizontal asymptote =
`\lim_(n \to \infty) f(x)`


`\lim_(n \to \infty) (9x^2-3x-8)/(4x^2-5x+3) =\lim_(n \to \infty) ((9x^2)/(x^2)-(3x)/(x^2)-(8)/(x^2))/((4x^2)/(x^2)-(5x)/(x^2)+(3)/(x^2)) =\lim_(n \to \infty) (9-(3)/(x)-(8)/(x^2))/(4-(5)/(x)+(3)/(x^2)) = (9-0-0)/(4-0+0)=(9)/(4)`