What is the end behavior of $y = 3 x^{4} + 6 x^{3} - x^{2} + 12$ $y = 3x^4 + 6x^3 - x^2 + 12$ ?

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What is the end behavior of $y = 3 x^{4} + 6 x^{3} - x^{2} + 12$ $y = 3x^4 + 6x^3 - x^2 + 12$ ?

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Answer 1 · 2018-06-22T13:29:11

I usually hear this called the asymptotic behavior. Big word, sounds smarter.

We have a leading term $3 x^{4}$ $3x^4$ with a positive coefficient times an even power of $x$ $x$ . So as $x \to - \infty$ $x to -infty$ or $x \to + \infty$ $x to +infty$ we get $y \to + \infty .$ $y to +infty.$

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What is the end behavior of $y = 3 x^{4} + 6 x^{3} - x^{2} + 12$ $y = 3x^4 + 6x^3 - x^2 + 12$ ?

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What is the end behavior of y=3x4+6x3−x2+12y = 3x^4 + 6x^3 - x^2 + 12?

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What is the end behavior of $y = 3 x^{4} + 6 x^{3} - x^{2} + 12$ $y = 3x^4 + 6x^3 - x^2 + 12$ ?