Question

At which values of x does the graph of have a vertical asymptote? Check all that apply.

–4
–1
1
2
4

Answer 1

I don’t see the function or graph you mean — can you paste the expression (or an image of the graph)?

In general, to decide which x-values from your list are vertical asymptotes:

1. Factor the rational function’s numerator and denominator.
2. Cancel any common factors. A cancelled factor (same zero in numerator and denominator) gives a hole, not a vertical asymptote.
3. The remaining zeros of the denominator are vertical asymptotes (regardless of multiplicity).

So for each candidate x = -4, -1, 1, 2, 4: check whether that x makes the original denominator 0 and whether the corresponding factor cancels with the numerator. Send the function and I’ll check them and mark which apply.