Vertical Asymptotes:

f(x)= x-4/x(x-4) . x-4 is a common factor in the numerator and denominator so this has no asymptote right? Or would it be 4? Can somebody help?

Question

Vertical Asymptotes:

f(x)= x-4/x(x-4) . x-4 is a common factor in the numerator and denominator so this has no asymptote right? Or would it be 4? Can somebody help?

e.mccormick · Answer

A common factor is a removable hole.  Not an asymptote.

anonymous · Answer

The common factor leaves a hole, but the x in the denominator does create a vertical and horizontal asymptote.

precal · Answer

|dw:1367974960441:dw|I believe your graph looks like this

anonymous · Answer

How do you find the asymptote then?

e.mccormick · Answer

There is still the x to deal with.

precal · Answer

vertical asymptote - solve the denominator for zero
horizontal asymptotes has rules (about 3 of them) it depends on the degree of the top and bottom

precal · Answer

|dw:1367975216729:dw|