Find any holes of the function

Question

f(x)=      8

       - --------

            x-6

 

A. There are no holes

B. x=6

C. x=4/3

D. x=-4/3

E. x=-6

F. None of the above

Answer 1

Gaps occur when the denominator equals zero. This is because anything divided by zero is undefined, so the function wouldn't have a value at that point.

 

x - 6 = 0

x = 6

==> B

Answer 2

No holes. (answer A)  There are no denominator factors that divide out.  The graph of the function has an asymptote at x = 6, but 6 is not a hole.