f(x) = -5(x + 7)(x - 2) / (x - 6)(x - 2)

Question

f(x) = −5(x + 7)(x − 2)
           (x − 6)(x − 2)

 

Identify any vertical asymptotes and horizontal asymptotes. (Enter your answers as comma-separated lists of equations. If an answer does not exist, enter DNE.)

 

Identify any holes if there are any.

Answer 1

I see you have the factors.  Great.  Not that there is a pair that are equal.  If these are divided out, we get:

 

     f(x) = −5(x + 7)

                   (x − 6)           Since, if we let x-> 6, f(x) -> ∞ since the denominator becomes 0, the vertical asymptote is the equation x = 6.  Also, since we have eliminated x-2, then x-2 = 0, or x = 2, is the hole.

 

If you were to sketch the graph of the original function, you would see the vertical asymptote at x = 6, and a hole at x = 2.