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.

Give a polynomial a big enough input and every term but one becomes petty cash. Two facts you can read at a glance, the degree’s parity and the leading coefficient’s sign, settle what both ends of the graph do. The traps come from reading the wrong term, and from asking end behavior questions it cannot answer.

8 STEPS · 6 QUICK CHECKS · LEADING TERM · PARITY · SIGN · LIMIT NOTATION · v2

large |x| → the leading term decides

Before you start

What you're looking at

A polynomial graph whose viewing window zooms outward, beside a table comparing term sizes at large inputs.

The question

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

Watch for

How the leading term overwhelms the others as the input grows, and how degree parity and leading sign set the two ends.

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