Question

Find the vertical asymptotes, if any, of the graph of the rational function. Show your work.


f(x) = (x-4)/(x(x-4))


(x-4)/x(x-4) the common factors cancel out and all is left is f(x)= 1/x...
how do I solve this problem?

Answer 1

vertical asymptotes occur where the denominator is zero and the numerator is not.

So, your graph has a vertical asymptote at x=0

try entering your function at wolframalpha.com to see its graph, and other information.

Note that as long as x≠4, f(x) = 1/x

There is a hole at x=4, because then f(x) = 0/0 which is undefined.