Given fx 2x2 8x10x23x18 a What is are the xintercepts b What

Given f(x)= (2x^2 -8x-10/x^2-3x-18) (a) What is (are) the x-intercept(s)? (b) What is (are) the y-intercept(s)? (c) What is (are) the vertical asymptote(s)?(d) What is (are) the horizontal asymptote(s)?

Solution

f(x)= (2x^2 -8x-10/x^2-3x-18)

a) x intercept : plug f(x) =0

2x^2 - 8x -10 =0

x^2 - 4x - 5 =0 ; x^2 -5x +x -5 =0

x(x-5) +1(x-5) =0 ; (x+1)(x -5)

x intercepts : x= -1 , x= 5

b) y intercepts : plug x=0 in f(x)

f(0) = -10/-18 = 5/9

c) Vertical asymtotes: Plug denominator =0

x^2 - 3x -18 =0 ; x^2 -6x +3x -18 =0

(x-6)(x+3) =0

x = 6 ; x= -3

d) Horizontal asymtote:

y = coeffcient ofx^2 in num/ coeffcient ofx^2 in den.

y = 2/1 = 2

y = 2