Let's Try It in Our Own Words
If a friend came up to you and asked "When does a rational function have a vertical asymptote at 𝑥=𝑐?", how would you describe the rule?
If 𝑥=𝑐 is a real zero of the denominator but not the numerator, or if 𝑥=𝑐 is a zero of the denominator and the numerator but the multiplicity is greater as a zero of the denominator.
If a friend came up to you and asked "When does a rational function have a hole at 𝑥=𝑐?", how would you describe the rule?
If 𝑥=𝑐 is a zero of the numerator and denominator and the multiplicity of that zero in the numerator is greater than or equal to the multiplicity of that zero in the denominator.