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Mathematics · L3 · Vertical Asymptote or Hole?

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A decision tree for classifying each zero of a rational function's denominator as either a hole or a vertical asymptote.

by @openstemUpdated Mathematics
✍️ Rational function f(x) = p(x)/q(x)Factor p(x) and q(x) completelyFor a zero x = a of q(x): does the factor (x − a) also appear in p(x)?🕳️ Hole at x = a📈 Vertical asymptote at x = aGraph has one missing point, not a breakGraph shoots to +∞ or −∞ near x = aYes, it cancelsNo, only in denominator

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