What is the equation of the horizontal asymptote of the function `f(x)=((2x-1)(x+3))/((x+3)^(2))`?

Options

A. `y=-9`
B. `y=-3`
C. `y=0`
D. `y=2'

Answer

D

Explanation

To find the horizontal asymptote, you need to see what happens when x gets must larger `(to oo)` or much `(to -oo)`. With the numerator and denominator expanded, `f(x)=(2x^(2)+5x-3)/(x^(2)+6x+9)`. Divide both by `x^(2)` to see that y approaches 2 as x gets much bigger or smaller.