Interpret terms, factors, and coefficients in polynomial and rational expressions.
Classify each rational denominator zero as a hole or vertical asymptote
Problem
For \(f(x)~=~1/(x~-~4)\), analyze each denominator factor and zero. State any numerator match, cancellation status, reduced formula, discontinuity, and domain exclusion.
Big Picture
What this problem is really about
Factor first, record every original denominator zero, and then look for matching numerator factors. Cancellation determines the type of discontinuity, not whether the input is excluded: a canceled zero leaves a removable hole, while an uncanceled denominator zero makes the quotient unbounded and creates a vertical asymptote. In either case, the original zero stays outside the domain.
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