What is the end behavior of f(x)=x3+1?

1 Answer
mason m
Nov 21, 2015

As x→∞,f(x)→∞; as x→−∞,f(x)→−∞.

Explanation:

A good way to test this is to plug in increasingly larger numbers in both the positive and negative directions.

For example, if x=1000,f(x)=1000000001. It is clear that f(x) will only keep increasing towards positive infinity if you plug in greater and greater positive numbers.

If you try negative numbers: x=−1000,f(x)=−999999999.

The negative number, when cubed, will always result in an negative number again. These numbers will get closer and closer to −∞.

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