How do you identify all vertical asymptotes for f(x)=1-3/(x-3)?

Jan 1, 2017

vertical asymptote at x = 3

Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote.

solve: $x - 3 = 0 \Rightarrow x = 3 \text{ is the asymptote}$

If you prefer you could consider f(x) as

$f \left(x\right) = \frac{x - 3}{x - 3} - \frac{3}{x - 3} = \frac{x - 6}{x - 3}$

The end result is the same.
graph{(x-6)/(x-3) [-10, 10, -5, 5]}