Advanced functions

A function's end behavior describes what happens to its output as the input grows very large or very small in either direction: it might grow without bound, like x^2 growing forever as x moves away from 0; level off, like f(x) = 1/x getting closer and closer to 0 without ever reaching it; or oscillate, like sin(x) repeating up and down between -1 and 1 forever. Piecewise, rational, and radical functions each behave differently near the values where they're undefined or where their pieces meet, so sketching one well means checking domain restrictions, intercepts, and end behavior together rather than plotting points one at a time.

This explanation is AI-generated and can occasionally be wrong. 🚩 Report