What is the end behavior of the graph of $f(x)=3x^4+7x^3+4x-4$ ?

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Answer 1 · 2014-10-18T23:59:03

$lim_{x to infty}f(x)=lim_{x to infty}(3x^4+7x^3+4x-4)$

by factoring out $x^4$ ,

$=lim_{x to infty}[x^4(3+7/x+4/x^3-4/x^4)]$

$=(+infty)^4(3+0+0-0)=+infty$

Similarly,

$lim_{x to-infty}f(x)=lim_{x to-infty}(3x^4+7x^3+4x-4)$

by factoring out $x^4$ ,

$=lim_{x to-infty}[x^4(3+7/x+4/x^3-4/x^4)]$

$=(-infty)^4(3+0+0-0)=+infty$

Hence, the function approaches $+infty$ on both ends.

I hope that this was helpful.

What is the end behavior of the graph of f(x)=3x^4+7x^3+4x-4f(x)=3x^4+7x^3+4x-4?