Question

If the line x=1 is a vertical asymptote of y=f(x), then f is not defined at 1. The questions asks true or false, and I know that the statement is false. I do need a counterexample and am struggling to think of one!

Answer 1

As x approaches 1 from either side, then f(x) will either approach infinity or negative infinity. So this means that f(x) is not defined at x = 1. So the statement is true.

Answer 2

Hmmm the textbook says that the statement is false. Could a step function be a counterexample?

Answer 3

If you have a step function with a vertical asymptote of x=1, you'll still have f(x) not defined at x = 1

Answer 4

The vertical asymptote exists because of a division by zero error, which is why it's not defined at that value