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.
Far from zero a polynomial behaves like its leading term, so a fraction made of two polynomials behaves like a fraction made of two leading terms. Compare those two degrees and every question about the ends is answered. Eleven short steps; press Next for each one.
end behavior = leading term ÷ leading term
Before you start
What you're looking at
A fraction of two polynomials, worked out at large inputs and then plotted with the line its ends settle on.
The question
For large inputs, which grows faster: the top, the bottom, or neither?