Question

Which statement describes the graph of the function?
The function has holes when x = 0 and x = 4.
The function has vertical asymptotes when x = 0 and x = 4.
The function has a vertical asymptote when x = 0 and a hole when x = 4.
The function has a hole when x = 0 and a vertical asymptote when x = 4.

Answer 1

I don’t see the function or its graph — can you paste the formula or an image of the graph?

Meanwhile, here are the rules so you can check quickly:
- A hole at x = a occurs when (x − a) is a factor of both numerator and denominator (it cancels).
- A vertical asymptote at x = a occurs when (x − a) is a factor of the denominator that does not cancel with the numerator.

Examples:
- Holes at 0 and 4: f(x) = (x(x−4))/(x(x−4)) (simplifies to 1 but has holes at 0 and 4).
- Asymptotes at 0 and 4: f(x) = 1/(x(x−4)).
- Asymptote at 0, hole at 4: f(x) = (x−4)/(x(x−4)) = 1/x (hole at 4).
- Hole at 0, asymptote at 4: f(x) = x/(x(x−4)) = 1/(x−4) (hole at 0).

If you share the function or the graph, I’ll pick the correct statement.