Question

The graph of f(x)= (x^2-2x-8)/(x+6) has which of the following?

a. point discontinuity
b. vertical asymptote
c. both of the above
d. neither of the above

I'm stuck between b and c. I know that the vertical asymptote is x=-6. Help?

Answer 1

f(x)= (x^2-2x-8)/(x+6)
to have a point discontinuity, (x+6) should have been a factor of the numerator and cancelled out.
e.g. if g(x) = (x^2 - x - 12)/(x-4)
g(x) = (x-4)(x+3)/(x-4)
= x+3, x ≠ 4

There would have been a discontinuity at the point (4,7)

So in your question , we should just go with b)

Answer 2

Ohhh okay thank you for explaining