**How do you determine the end behavior of a function? And, what does this mean?**

When looking at a graph, the “end behavior” is referring to what is happening all the way to the far left of the graph **and** all the way to the far right of the graph. Your goal is to analyze the y-value (height or function value) of the function when x is really large and negative, and then again when x is really large and positive. What is the pattern on each end? What is the “end behavior”?

Notationally, we are thinking:

- As x → -∞, y → ?
- As x → +∞, y → ?

OK, so let’s try this on a polynomial example:

**Q: What is the end behavior of the function y=5x**^{3}+7x^{2}-2x-1

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