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.