Verified answer

vertical:

-7x-2 = 0

-7x = 2

x = -2/7

2x-7 = 0

2x = 7

x = 7/2

Horizontal: the highest power of x on the top and on the bottom are the same (x^2), so it would be the coefficient on the top over the coefficient on the bottom.

If you foiled the top you would get x^2... and on the bottom -14x^2...

so -1/14 is the horizontal asymptote.

f(x)=(x^2-5x-14)/(-7x-2)(2x-7)

Vertical asymptote means that for a determined x value, y goes to infinite. So the denominator must be null (but not so for the numberator)

(-7x-2)(2x-7)=0

x=-2/7

x=7/2

for x that goes to -2/7 f(x) goes to -infinite

for x that goes to 7/2 f(x) goes to -infinite

We can find horizontal asyntotes by making x go to + or - infinite: so we put x^2 in evidence

f(x)=x^2(1-5/x-14/x^2)/x^2(-14+45/x+14/x^2)=-1/14

this is the horizontal asyntote