Mistake Master
Mistake Master · AP Precalculus · Unit 1 · Step-Through Animation
One Fraction Decides Both Ends
You'll learnto find a rational function's end behavior by comparing the degrees of its top and bottom.
For large |x| a polynomial collapses to its leading term, so a ratio of polynomials collapses to a ratio of leading terms. Compare two degrees and every end-behavior question is answered: a horizontal line at zero, a horizontal line at the coefficient ratio, or unbounded growth along a quotient. And the horizontal line is a description of the ends, never a fence the graph may not cross.
end behavior = leading term ÷ leading term
Before you start
What you're looking at
A rational function with the leading terms of its numerator and denominator highlighted, and a horizontal asymptote drawn.
The question
For large inputs, which grows faster — the top, the bottom, or neither?
Watch for
The three cases (bottom grows faster, tie, top grows faster) — and that the graph is allowed to cross a horizontal asymptote.
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