Vertical Asymptote vs Removable Discontinuity
A researcher investigates the behavior of the rational function . Upon graphing the function, the student identifies a vertical asymptote at . After further analysis, it turns out that this is actually a removable discontinuity. What mistake did the student make in the analysis?
Failing to factor and simplify the rational function, thereby mistaking a removable discontinuity (a hole) for a vertical asymptote at .
Miscomputing the horizontal asymptote by incorrectly dividing the highest degree terms.
Applying long division improperly, which resulted in an inaccurate description of the function’s end behavior.
Erroneously assuming that both the numerator and denominator approach infinity at the same rate, misidentifying the asymptotic behavior.
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