Far Enough Out, Only the Leading Term Survives

You'll learnto predict what both ends of a polynomial graph do from just its leading term.

Feed a polynomial a big enough input and every term but one stops mattering. Two facts you can read at a glance, whether the degree is even or odd and whether the leading coefficient is positive or negative, settle what both ends of the graph do. Eleven short steps; press Next for each one.

11 STEPS · 6 QUICK CHECKS · LEADING TERM · PARITY · SIGN · LIMIT NOTATION · v3

large |x| → the leading term decides

Before you start

What you're looking at

Two terms of one polynomial raced against each other, then four small graphs showing what each kind of end does.

The question

Far from zero, which single term decides the shape of each end?

Step 1 / 11