How do you find the end behavior of $f (x) = - x^{4} + x^{2}$ $f(x)= -x^4+x^2$ ?

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How do you find the end behavior of $f (x) = - x^{4} + x^{2}$ $f(x)= -x^4+x^2$ ?

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Answer 1 · 2015-07-08T01:28:29

$f (x) \to - \infty$ $f(x)->-\infty$ as $x \to \pm \infty$ $x->\pm \infty$

Explanation:

The function $f (x) = - x^{4} + x^{2}$ $f(x)=-x^4+x^2$ is a polynomial with a degree of 4 (the largest exponent), which is even. Also, the coefficient of the highest powered term is negative.

These facts are enough to conclude that $f (x) \to - \infty$ $f(x)->-\infty$ as $x \to \pm \infty$ $x->\pm \infty$ . This means that the graph of $f$ $f$ goes down forever and ever without bound as $| x |$ $|x|$ gets larger and larger without bound. To be a bit more precise, the graph of $f$ $f$ will go below and stay below any given horizontal line by choosing $x$ $x$ to be sufficiently far from zero.

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How do you find the end behavior of $f (x) = - x^{4} + x^{2}$ $f(x)= -x^4+x^2$ ?

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How do you find the end behavior of f(x)= -x^4+x^2f(x)=−x4+x2f(x)= -x^4+x^2?

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How do you find the end behavior of $f (x) = - x^{4} + x^{2}$ $f(x)= -x^4+x^2$ ?