What can you say about the end behavior of the function f(x)=-4x^6+6x^2-52

As x gets smaller, pointing to negative infinity, the value of f decreses, pointing to negative infinity.

As x gets increases, pointing to positve infinity, the value of f decreses, pointing to negative infinity.

Step-by-step explanation:

To find the end behaviour of a function f(x), we calculate these following limits:

And

In this question:

At negative infinity:

When the variable points to infinity, we only consider the term with the highest exponent. So

So as x gets smaller, pointing to negative infinity, the value of f decreses, pointing to negative infinity.

Positive infinity:

So as x gets increases, pointing to positve infinity, the value of f decreses, pointing to negative infinity.

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step-by-step explanation:

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