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What is the end behavior of $f (x) = - 3 x^{5} - 4 x^{2} + 3$ $f(x)=-3x^5-4x^2+3$ ?

1 Answer

Aug 30, 2017

$f (x) \to + \infty as x \to - \infty$ $f(x)rarr+oo" as "xrarr-oo$
$f (x) \to - \infty as x \to + \infty$ $f(x)rarr-oo" as "xrarr+oo$

Explanation:

When dealing with end behavior, only the term with the highest degree is significant (because as $x \to \pm \infty$ $xrarr+-oo$ its magnitude will exceed those of all other terms).

As $x \to - \infty$ $xrarr-oo$
$XXX x^{5} \to - \infty$ $color(white)("XXX")x^5rarr -oo$
and
$XXX - 3 x^{5} \to + \infty$ $color(white)("XXX")-3x^5rarr +oo$

Asw $x \to + \infty$ $xrarr+oo$
$XXX x^{5} \to + \infty$ $color(white)("XXX")x^5rarr +oo$
and
$XXX - 3 x^{5} \to - \infty$ $color(white)("XXX")-3x^5rarr -oo$

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