Answer:
Vertical aymptotes at x= -4 and x=6
horizontal asymptote at y=0
Step-by-step explanation:
[tex]f(x)= \frac{-7}{x^2-2x-24}[/tex]
To find out vertical asymptote we take the denominator =0 and solve for x
x^2-2x-24=0
sum = -2 and product = -24
4 * (-6) = -24
4 - 6 = -2
(x+4)(x-6)=0
Now we set each factor =0 and solve for x
x+ 4=0 and x-6=0
x= -4 and x=6
Vertical aymptotes at x= -4 and x=6
Now we find horizontal asymptote
The degree of numerator is 0
degree of denominator is 2
Degree of numerator is less than the degree of denominator then horizontal asymotote is y=0
0 < 2 so horizontal asymptote at y=0
