Relate a function's domain to its equation, graph, and context, especially when model choice matters.
Match a domain restriction to the graph feature it creates
Problem
For a rational function, what graph feature matches this restriction: \(x=4\) excluded by uncanceled denominator?
Big Picture
What this problem is really about
An excluded rational input can create different graph features, so ask what happened to the denominator factor. If it survives simplification, nearby denominators shrink toward zero while a nonzero numerator remains, sending output magnitudes without bound. Cancellation would instead make the break removable; that contrast distinguishes the two discontinuity types.
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