What is the end behavior of #f(x) = x^3 + 1#?

Answer 1

As #xrarroo,f(x)rarroo#; as #xrarr-oo,f(x)rarr-oo#.

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 #-oo#.

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Answer 2

Theodore Amidon

The end behavior of ( f(x) = x^3 + 1 ) is as follows:

As ( x ) approaches negative infinity, ( f(x) ) approaches negative infinity. As ( x ) approaches positive infinity, ( f(x) ) approaches positive infinity.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.