Question

Which of the following functions have graphs that contain vertical asymptotes?

Answer 1

A vertical asymptotic is a point at which y approaches positive or negative infinite, or both, and y is undefined at that x value.

Of the options, the reciprocal has a vertical asymptote. When approaches zero, y approaches 1÷0, or infinite.
The logarithmic function also has a vertical asymptote at x=0. Let's use f(x) =log base 10 (x) as an example. This function describes the exponent you'd have to put on 10 to get x. When x=0, we have a bit of a problem. What power can you raise 10 to to get 0? The answer is negative infinite, which would be
1/ (10^∞) = 0.