Interpret terms, factors, and coefficients in polynomial and rational expressions.
Audit numerator zeros for rational x-intercepts or holes
Problem
For \(f(x)~=~(x~-~3)/(x~+~2)\), audit every numerator zero against the denominator. State the domain exclusion, cancellation status, and resulting \(x\text{-}\text{intercept}\) or hole.
Big Picture
What this problem is really about
Treat each numerator zero as a candidate graph feature, then audit it in the original denominator. A nonzero denominator makes the rational output genuinely zero and produces an x-intercept. If the same factor also appears below and cancels, the input remains excluded and becomes a hole instead, so numerator information alone is never enough.
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