consider the following Find the intercepts horizontal smalle

consider the following.

Find the intercepts

horizontal: (smaller value)

horivontal: (larger value)

vertical intercept

Find the verticla asymptote and horizontal asymptote

f(x)=2x²-18/x²+x-2

f(x)= (2x²-18)/(x²+x-2)

Intercepts : xintercept ; 2x^2 -18 =0 ; x = -3,3

smaller value x = -3 ; larger value : x =3

y intercepts : plug x =0 ; f(0) = -18/-2 = 9

(0, 9)

Vertiical asymtote : x^2 + x -2 =0

x^2 +2x -x -2 =0 ; x(x+2) -1(x+2) =0

( x -1)(x +2) =0 ; x = 1 ; x = -2

Horizontal asymtote : y = 2x^2/x = 2

y = 2